"While I think [the Thanator] was a neat looking creature, it exhibits ‘Hollywood super-predator syndrome’, and acts like an unstoppable, drug-fuelled, psychotic whirlwind, smashing through vegetation, tearing tree roots up, and altogether doing everything possible in order to kill and eat the object of its attention. It’s not even deterred by a barrage of automatic gunfire, and almost pursues Jake right off the end of a cliff (he jumps off to land in the waterfall splash-pool below)."
Our intrepid young adventurers are exploring their new unknown land for whatever reason it may be: money, pursuit of knowledge, or simply by accident (a quest for survival). In any case, they are unaccustomed to the land, but aren't exactly smart about being careful. Namely, they run into some monstrous beast that wants only one thing from them: lunch. After a dangerous escape (someone will probably be killed), the explorers dust themselves off, maybe laugh nervously, and try to get as far away from that thing as possible. No harm done, time to focus on getting to the shelter or something, right?
But wait, what's that sound? Is it following them? Through rivers and mountains and who knows what else?
You bet. Seems like this thing just won't give up until it has another taste of human. No matter how long it goes without a meal.
Basically, this predator will hunt the protagonists far beyond the call of common sense or even instinct. Be it through fierce jungles, caves, canyons. Once the climax comes by, the beast will most likely be right there ready for one Final Battle. If the heroes manage to find shelter, the predator(s) will go through an extreme amount of effort to break windows, unlock doors, or learn to bypass complicated security measures and then bash through a wall anyway to get to its prey. A situation like this might have you thinking that it'd be more productive to just find something else to eat. Sometimes it's explained away by stating that they've got human intelligence, but that just raises further questions about why an intelligent predator would expend so much effort to eat something that keeps eluding them. You might find an ecologist tearfully screaming that nobody, animal or human, would be this vindictively persistent just for one difficult meal.
But there's a reason this trope can work so very well. Note the word human intelligence. "Persistence hunting" isn't only a scarily good hunting strategy, provided the predator has enough stamina to keep chasing until the prey doesn't have the strength to keep running, it's also our strategy, both in hunting and escaping (waiting for the predator to give up). The use of this trope instantly makes the 'dumb animal' a credible threat and Worthy Opponent, since we don't have the option of outfoxing it until it gives up and goes away. No, this is something smart enough to see through our strategems, that won't fall prey to Attention Deficit... Ooh, Shiny! and stop chasing us, and will continue the hunt even as we tire. It's clearly going to come down to a climactic battle of man vs. nature. Exciting, no?
Amusingly, this is one handwave that often wouldn't have been necessary — it's a well known fact among biologists that intelligent predators can and will hunt for fun, even if they aren't hungry. For example, dolphins will torture and kill smaller breeds of dolphins as well as band together to gang rape young female dolphins — and males, they aren't picky; this goes double for orcas, which have been known to throw live seals around for hours on end, occasionally releasing them once they're done. Oh, and let's not forget about a few humans' habits.
In practice, this is the animal version of the Implacable Man. The inversion is Animal Nemesis. Compare Attack! Attack! Attack!, when the animal fights irrationally. Usually happens in places where Everything Is Trying to Kill You. Biological equivalent of the Spiteful A.I.. The entire universe can be like this to The Chew Toy or Butt Monkey. If this beast appears at the end to chase the villain away, it's Exit, Pursued by a Bear. This trope has nothing to do with Predator, although that one is super persistent, albeit for different reasons.
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Anime & Manga
Dragon Ball Z had an amazing example of this. Young Gohan was sent on survival training with little more than a sword. Eventually, he gets the hang of it. And apparently gets chased by a Tyrannosaurus Rex every morning. Not only does the T. Rex never get Gohan, every morning he knocks him out and he slices off part of his tail and eats it. And yet, despite his prey eating HIM every morning, the T. Rex continues to hunt Gohan. (In the beginning, anyway. Eventually, it starts running ''away'' from him.)
Gyo features numerous dangerous aquatic creatures trying to prey on the human populace, but one of the most notable and driven examples is the land-mobile great white shark which attacks the protagonists, which goes to quite extraordinary lengths in its attempt to devour the heroes. Though the circumstances aren't entirely clear, this example may be justified, as the fish in question have been cybernetically (and, it is strongly implied, supernaturally) augmented for the specific purpose of killing and inflicting terror on humans; many are already dead or dying and seem more driven on by the machines attached to them rather than any natural urge to feed.
Tower of God has the Bull, an amphibious predator that settled in the testing grounds and constantly hunted examinees. Though when it attacks the main characters, it's because it's being mind-controlled by Ren.
Justified/Invoked with the Abyss Eaters, from Claymore, as they are conditioned to crave the flesh of one particular target. Said target is much, much stronger than them, but their persistence wears him down until he dies a Death of a Thousand Cuts after months in a constant state of battle.
No one is quite sure why the Titans of Attack on Titan prey on humans. It's been shown that they don't even need to eat humans to survive.
The most basic definition of an Aberrant Titan seems to be one whose persistence is predicated on some factor other than "closest humans nearby". And a Titan showing priorities other than eating humans at all is considered very strong evidence for sapience.
In one issue of Xenozoic Tales, Jack has been stranded in the wilderness without weapons and has the misfortune to attract the attention of a cutter (Allosaurus) that keeps coming after him, over and over again. Justified in this case because the cutter has an injured jaw and isn't capable of hunting its normal prey. Jack is the first animal it has encountered in some time that combines being large enough to hunt with being defenseless. Just his luck!
In Pocket God, a shark with a laser beam on its back is a regular adversary for the pygmies. Its persistence is lampshaded in one issue.
Films — Animated
Not exactly a predator, but the prehistoric squirrel in Ice Age is pretty persistent about getting That One Nut; his attempts, and subsequent failures, to eat is a Running Gag.
And in the third film, we have Rudy.
The crocodile from Peter Pan. Justified with the bit of backstory that the croc had eaten Hook's amputated hand and liked the taste so much that he wanted the rest of the dish.
The shark which manages to flop very fast across an unclear distance of land and right into a volcano in pursuit of the very small lemur Mort in Madagascar: Escape 2 Africa.
The Albertosaurus from the docu-movie March of the Dinosaurs. It pursues the small Scar and his sick companion even after having caught on fire, being washed away by a flood of mud, and getting knocked out, and continues to grasp its victim with its jaws while the rest of him is hanging down from a cliff! And to think it just could have gone back to its pack who had tons of fresh meat at the ready.
Maximus the Horse from Tangled goes to incredible lengths to chase Flynn Rider, even getting into a swordfight with him. Justified in that he isn't looking for a meal, but a criminal at large, being essentially a police horse.
Sharptooth (Tyrannosaur) from the first The Land Before Time hunted the dinosaur heroes through mountains and a desert. Land Before Time 5 The Mysterious Island shows that Sharpteeth are intelligent enough to talk (It's in a language the herbivores can't understand. Chomper is apparently bilingual.), so it could have been a particularly cruel and sadistic Sharptooth. Possibly justified in that the environment is dying and prey is extremely scarce, along with baby dinosaurs being easy prey compared to adults.
The wolf from The Rugrats Movie stalks the babies and Angelica through most of the movie.
Films — Live-Action
This trope is the premise of The Ghost and the Darkness. This is also a true story; the lions are stuffed and on display in the natural science museum in Chicago. Later studies have suggested that between the two lions, they only ate some 40 people; still a lot, but not the 140 originally claimed.
In Kaw, Creepy Crows get infected with Mad Cow (?!) disease after eating clearly diseased rotting cow flesh. As soon as they go crazy, they decide to exclusively go for the human protagonists (not even any other areas, just those few people). This includes waiting on a bus while the the humans cry and then throwing rocks at the bus in a desperate attempt to get inside. Later, they slam themselves against a diner in order to get in and eat the people inside, before they inexplicably die. You'd think there weren't any animals in the forest. Subverted in that the super persistent predators starve to death, just as they would in real life.
Shockingly averted in the (surprisingly good) reimagining of The Land That Time Forgot (which starred and was directed by C. Thomas Howell) in which the Rex only chases the humans when they enter its territory to steal food, and all it does is just try to run them off.
Justified in Crocodile (but not so much the Sci-Fi Original sequels third and onward), featuring a crocodile (giant, naturally) pursuing a group of half-dressed teenagers. One of them had one of her eggs in his backpack, fueling her maternal rage. The survivors are allowed to leave when they return it. However, while real life crocodiles actually do have fairly strong protective instincts, they wouldn't chase after someone, and if a nest robber got away from it, it's not going to bother to chase it down.
The xenomorphs of Alien will hunt down and kill (or capture for impregnation) anything and everything near them. One theory raised by those making the movie was that the aliens were created as weapons of war, so that would also make their Kill 'em All actions plausible. The prequel Prometheus justifies the xenomorphs' persistence with The Revealthat they are merely a by-product of the Engineers' bio-weapon. Like everything else spawned from the black goo, the xenomorphs' only purpose is to wipe out all life.
While the shark in Jaws is not much of an example, as it behaved much like an actual predator, the sequels play this very straight. Taken to ludicrous extremes in Jaws: The Revenge, apparently tracking down people over hundreds of miles (while our protagonists are in an airplane) in order to kill them in revenge for their father having killed a couple of other sharks a decade earlier.
Jurassic Park teetered over the edge of this trope for two films:
In the first, the T. Rex and the "velociraptors" aren't following the humans as much as chancing upon them and chasing them a bit. The first encounter with the T. Rex plays this trope quite straight, giving up only after any real animal would've given up, not mentioning that at the speeds that the jeep is going a Tyrannosaurus would be suicidal to run at, let alone have the physique for. However, both the T. Rex and the raptors in the original novel are extremely persistent.
Unusually, the original film shows both the rex and the raptors losing all interest in humans when the chance to attack a rival predator, i.e. each other, comes along. As both had recently eaten, territoriality trumped hunger.
In the third, however, they just throw reason to the wind, and have all the dinosaurid predators behave this way. The Spinosaurus chase the protagonists about a mile farther than reason would allow. One would think that there weren't any other dinosaurs around, or that it was just that cruel. They also stumble upon a Tyrannosaurus standing over a dead dino (looks like it's scavenging) with plenty of meat, but when it sees the humans, it naturally starts pursuing them instead. Which incidentally leads it to the Spinosaurus, whom it engages and dies. It might have perceived them as a threat to its meal and be chasing them off... in which case it ought to have stopped chasing them as soon as they were out of sight and gone back to its food. The Velociraptors of this film, however, were chasing the heroes because one of them secretly stole their eggs.
While all of the predators of King Kong's Skull Island seemed to want to try out the new taste sensation of humanity more than the next one, none were worse than the T-RexT. RexV. Rex who actually runs after Ann Darrow with the corpse of a current kill in his mouth. Some of the V. Rexes on the island actually sacrifice themselves in their attempts to kill her. And when given the chance to bite Kong versus swallowing Ann, they always went for Ann.
The Venatosaurus raptor-pack, which idiotically tried to chomp humans in the middle of a Brontosaurus stampede, then persisted in chasing down hapless cameramen, rather than gorging on several thousand tons of fresh bronto meat that was lying there waiting for them.
The sharks in Deep Blue Sea. Tom Jane even points out that sharks don't particularly like the taste of people. Justified because eating the people isn't the goal, getting them to open doors and flood the facility is. Although wiping them out is a beneficial bonus since no one else would know about the super intelligent sharks...
TV B-MovieThe Last Dinosaur has the titular titan, a T. Rex with Implacable Man tendencies, treat a group of explorers like this... at first. Then we see it kill and eat everything unlucky enough to cross its path. Implicitly, it's eaten most every other animal in the Lost World.
Used as padding in the new Star Trek film. Kirk is being chased by some shambling furry thing. Then a giant red ant bursts out of the ice, bites the furry thing, tosses it aside... and starts chasing Kirk. Even though the shambling furry thing was bigger (but still bite-sized to it) and it had already attacked it. Makes significantly more sense if you interpret the red creature as being territorial as opposed to hungry. It frequently stops to roar at Kirk, something a hunting animal is unlikely to do but an animal trying to intimidate a supposed threat might, and Spock Prime is able to run it off with a mere signal flare once it enters his territory, the cave.
The bear in The Edge was a perfect example of this trope.
The killer whale in Orca: The Killer Whale. Justified in that it was out for revenge, something dolphins regularly do in Real Life, though in the film it was portrayed as a male avenging his mate and child (making it more like an aquatic Death Wish than a Jaws imitator) when in reality it would be a whole pod avenging one of their friends.
Played with in the 2009 Land of the Lost movie. The resident T-Rex, Grumpy, actually is all set to give up on chasing Marshall, Will, and Holly after they prove to be more trouble than they're worth. That's until Dr. Marshall insults the T-Rex's intelligence, causing it to hold a grudge against him for the rest of the film.
Anaconda combines this with Artistic License - Biology, stating that the anaconda is some kind of Blood Knight that enjoys killing so much that it will regurgitate its latest meal just so it can hunt and kill again. Needless to say, no real reptile would waste energy like that. Anacondas and other giant snakes were once thought to do that, but it turns out they only regurgitate their food if they're overly threatened while lethargic (btw, the snake in the movie should find a safe place and go into a self-induced coma after eating just one guy, nevermind a whole boat), or because they're, y'know, getting sick off it. The sequel Anacondas: The Hunt for the Blood Orchid handwaves this by putting numerous snakes in the same small area due to a mating season being in progress. It's even pointed out that a single one shouldn't be a problem for quite a while after it has fed itself.
The titular pigeon from Pigeon: Impossibleas shown here — allowing a nuclear missile to blow up another country, all for just a bagel.
The baby Zillas in Godzilla (1998). As newly hatched animals, not only should their first priority be to feed themselves, which is easy given the abundance of available fish, but they should be starving and exhausted from the effort of hatching. Worse, they all start competing over an incredibly small number of people to eat (even at some points seeming to start fighting among themselves over who gets to eat the people).
Actually justified, as all fish is gone by the time they start chasing humans (who smell like fish).
The last stretch of Prophecy has the main cast dealing with a literal (mutated) Mama Bear that wants to get them no matter what.
The Tiger in Burning Bright. Justified in that the Tiger was starved for nearly a week, and there was no other food supply.
The Graboids in Tremors are willing to wait out for days, weeks, months to catch a prey marooned in high ground. It doesn't help that they learn very quickly, and sitting and waiting for trapped prey to move requires zero energy expenditure compared to searching all over the valley for food.
Justified in the TV series, where Jodie remarks that Graboids, or at least El Blanco, do prefer eating people over other potential prey.
El Blanco himself, in the third movie, seems to only go after Burt. Near the end it's revealed that El Blanco is just attracted to Burt's new sonic watch.
An inversion in Cool Hand Luke: when Luke escapes prison, he runs so persistently that the bloodhound trailing him runs itself to death.
The sea monsters in Deep Rising, who continue to relentlessly pursue the heroes despite suffering extreme gunfire trauma from doing so every time. One might also wonder why the entire creature attacked the ship in the first place seemingly in pursuit of a bunch of microscopic humans.
The Grey features a pack of Savage Wolves as a central plot point. Justified, because the humans were unknowingly moving deeper into the wolves' territory. The last guy finds himself in their den.
Justified in Red Planet with AMEE, a dog-like robot borrowed from the Marines for the mission, whose processor gets damaged in the crash, and it classifies the astronauts as "foe". Not being an animal (or a living being), AMEE doesn't need to rest, feed, drink, or sleep. It runs on a fusion battery, so power is not an issue. It can chase them as long as it has to. AMEE follows classic guerilla tactics. The first thing it does is wound one of them to slow down the whole group and then follow, using its aerial drone to spy on the humans. Whenever a member of the group is separated, it moves in for the kill, making sure to broadcast the video of the murder to the rest of the group to demoralize them and incite panic.
Justified in Komodo. The komodos relentlessly pursue the protagonists, but there are several of them and they are stated to be starving.
The masked antagonists of The Purge qualify, as they assault a heavily-fortified McMansion to get at the nameless black guy instead of going after any other, far easier target.
Onibaba in Pacific Rim was very determined to kill a young Mako. It's implied, though, that being a memory, this scene wasn't meant to be a literal retelling of events but rather the skewed representation of a scared little girl in the middle of a Kaiju attack. Though it would be justified, since the kaiju are not natural predators, but bioweapons created solely to wipe out humanity. That means every single human, even a little girl, has to die.
In the shark horror film Bait 3 D, the sharks persistently hunt the surviving humans. It becomes more believable at the end when it's revealed that the sharks were actually trapped in the convenience store along with the people and couldn't just swim away.
In Godzilla (2014), Godzilla tracks the Mutos from one side of the Pacific to the other. Justifiedconsidering Godzilla considers the entire Earth its territory and the MUTOs are an active threat to the biosphere.
The Terminators can be considered mechanical versions of this, Predator Drones, so to say. They can't be bargained with; they can't be reasoned with. They don't feel pity, or remorse, or fear. And they absolutely will not stop, EVER, until you are DEAD. They are even worse than most examples, because they combine (at least) human-level intelligence with super-human resilience and strength.
The cannibals of The Colony never stop, despite the fact that chasing the protagonists is killing them off quickly. Perhaps justifiable since they really have no other source of food.
In Michael Crichton's Jurassic Park, Muldoon commented that the raptors were cruelly intelligent and liked to hunt for sport as much as for food. It was actually justified in the second book, which explained that because raptors were so intelligent, being born and raised without actual raptor "parents" to raise them properly turned them into violent and chaotic creatures.
Meanwhile, the Tyrannosaur seemed to be stalking Dr. Grant and the kids in particular, even leaving behind a Hadrosaur kill to pursue them down a river. It starts to become pretty obvious Rule of Scary when at one point it's waiting at the bottom of a waterfall with its jaws open, hoping they'll fall inside.
Happens in an utterly over-the-top way in Wraith Squadron, with an insect that supposedly follows mammalian prey it encounters... well, as far as it has to. (Even managing to sneak onto the heroes' spaceship.) The Storini Crystal Deceiver is said to paralyze its prey and eat them alive; victims can be saved if they are found before too much biomass has been devoured. The victim hears the creature in the walls, and ends up coating the entire room in plastic sealant to keep it out... only to hear it afterwards in the room. Subverted hilariously: the entire creature and the auditory hoax to go with it was made up as part of a practical joke, as the logical extreme of an Escalating War with a covert practical joker. And it's then mixed with a healthy dose of Fridge Terror, when Face and Phanan explain to the prankster that this was their LOWEST setting of payback.
Justified in the Artemis Fowl series with Trolls. Apparently to them, humans are by far the most deliciousest things ever, and after trying one, a troll will do anything to eat more. Also, as subterranean predators, they have extremely finely-tuned senses, so that exposure to the surface tends to cause them sensory overload which causes severe brain damage, usually removing most of their survival instinct.
In one of the AnimorphsMegamorphs books (a special event book in which all six characters narrate), they are transported back in time and find themselves battling a Tyrannosaurus Rex. While fleeing, they morph to escape, and Marco morphs into an osprey, his standard bird choice, that has both the ability to fly and should logically be too small to keep the predator's attention. However, instead of giving up once the already-small meal becomes an even smaller meal, as Marco logically expects it to do, the dinosaur keeps chasing him, and actually begin to tear apart trees that are standing in the way. Marco ultimately realizes that food has stopped being the point of the chase, and that the Rex is chasing him out of pure blood-lust and rage.
While they are humanoid, the trolls in R.A. Salvatore's Streams of Silver act like predators (they are trying to kill and eat the heroes, after all), and they are extremely persistent.
In Piers Anthony's Orn, one of the characters has a prolonged battle with a Tyrannosaurus, in the sense that they play an extended game of cat and mouse. The attempted justification for this is that the dinosaur has evolved the tactic of pursuing its meals relentlessly, thus ensuring that, eventually, it will eat. Which still doesn't make sense, as eventually it risks burning more calories trying to catch the prey than it'd get from eating it.
The Wisteron in The Elf Queen of Shannara, which pursues Wren and the other Elves any time they so much as put a toe outside of Arborlon, and flatly refuses to stay down. Justified, as like the other Shadowen on the island, it hates the Elves for creating it in the first place.
The Graak and the caulls in The Voyage of the Jerle Shannara also behave this way. It's justified in the case of the caulls, which are magically-altered mutantwolves designed to track their victims relentlessly. The Graak, a massive, bloody-minded dinosaur, doesn't have any justification for its behaviour, but is such a Primal Fear that it doesn't really need one.
The Tracker Jacker wasps of The Hunger Games. Their name is pretty self-explanatory, as they were bred to A) track down their prey and B) (hi)jack their victim's nervous system with their Grade A hallucinogenic venom. They home in on the first person they see and don't stop until said person is stung.
In Mockingjay, there were the lizard-mutts, which were engineered to hunt and kill Katniss specifically, but will viciously munch on anything or anyone in their way.
Gone to absolutely ridiculous and eventually cinematic extremes in David Fletcher's Hunted: A True Story of Survival, in which a literal Mama Bear goes after the writer for killing her cub and it only ends when the writer manages to crush the bear under tons of ice. The kicker? It's supposed to be based on a "true story".
The enormous Tyrannosaurus rex Moriarty in Dinoverse stalks the four teenagers-in-dinosaur-bodies for hundreds of miles after meeting them on a beach. Getting pulled into the ocean by an Elasmosaurus, having rocks flung into its face after an earthquake, and a flash flood do not deter him. Bertram gives a weak explanation by saying that since this group of animals would never normally travel together, they might signal disease. Certainly they're big enough to make a good meal, but this is a lot of effort, especially considering how easy it is to forage for food on the seashore. Mike, who's in the body of a T. rex himself, thinks that It's Personal.
TheRuum by Arthur Porges is all about this trope. The Ruum is a virtually unstoppable alien bio-mech creature which pursues the protagonist, Jim Irwin, until it finally catches him, only eventually releasing him due to him not falling within its strictly limited capture standards. A full story summary is available on The Other Wiki.
Live Action TV
Primeval has the Smilodon (very much at odds with what we know of the real animal, which had relatively short legs and heavy muscle attachment sites, indicating that it was a sprinter, not a distance runner) and the Gorgonopsid, depending on whether it was supposed to be deliberately chasing the kid or just randomly found him again. And true to their classic reputation, the raptors, who will follow you up elevators. And then there's that anomaly-jumping raptor from 3.10.
Justified with the Spinosaurus from episode 4.1, which pursues Connor and Abby for territorial reasons rather than to eat them.
Several of the cryptids featured in Lost Tapes play to this trope.
Inadvertently deconstructed in the Babylon 5 episode "Grey 17 Is Missing" with a craptastic alien "predator" called a Zarg straight out of MST3K. It wasn't stealthy, it wasn't intimidating, it wasn't even particularly original, and producer Straczynski has been known to say he wants to apologize to fans in person for it.
Played scarily straight with the ShadowBattlecrabs. Once they lock on to a target, they will never cease pursuit until it is destroyed. Seeing how they can easily overtake almost any other spaceship in the galaxy, they rarely have to resort to this.
Another scary one is the Na'ka'leen Feeder, who, unless you provide him food, will chase you everywhere to eat your memories. The Centauri quarantined its resource-rich after some of these beasts wiped out an entire colony, and news of one of those things having been shipped on the station had Londo barricade inside his quarters in terror until he was told it had been found and killed.
Terra Nova plays with this. In one sequence, a pair of Carnotaurus chase two jeeps up to the gates of the titular settlement, but when TN's defensive sonic weapons start firing, the dinosaurs decide to look for something easier to kill. The trope is later played straight with the fictional Slashers, which are really, really determined to get at the stranded kids in the broken down jeep, never mind those pesky assault rifles the kids have.
Lampshaded and subverted in the Star Trek: The Next Generation episode "Genesis". When Picard and Data find themselves cornered in the sickbay, with a de-evolved Worf pounding away at the non-functioning door holding him back, Picard wonders aloud if Worf sees them as prey. Data points out that there are other de-evolved crew members to eat that aren't behind thick metal doors that would be much easier to get to, so something else must be driving De-evolved!Worf on. Turns out, he's being driven by a mating instinct for a de-evolved Troi.
In one Garfield strip, a dog chases Garfield up a tree. Garfield wonders how long the dog will wait for him to come down before giving up and going home. When he looks down he sees that the dog has made itself comfortable with a recliner and a glass of lemonade.
In the Doctor Who radio serial "The Paradise of Death", the Gargan is a predator that ignores you unless you enter its territory (which it thoughtfully marks with rocks). If you do pass the rocks, it pursues you until it has eaten you.
Raksha (souleating Lovecraftian fae from Exalted) find human dreams and emotions especially tasty.
Likewise, there's Zsofika the Kite Flute, a Second Circle Demon known for choosing one target and chasing it every chance she gets until it's dead. It doesn't matter if you banish her or dispatch her back to Malfeas via copious stabbings — unless you find some way to permanently kill her, as long as she's in Creation and she's not bound to a task, she will be coming after you.
In Paranoia, a doberbot's combat programming works this way. "Attack someone until he dies. Attack someone else until he dies. Attack someone else until he dies..."
One of the Rolemaster supplements has rules for a thing called the "Black Reaper". Next to the description is also a short story featuring this monster: A demonic warrior clad in black armor and wielding a huge axe is disturbed when an adventurer decides to take a certain item from a treasure hoard. The thief and his companions manage to flee back to their boat and sail across the ocean for days, when suddenly the Black Reaper climbs up the anchor chain and finally kills him with his axe, taking the stolen item, ignoring everyone else, and begins to move back to its lair. The rules state that it can create passages through all but the hardest magical surfaces with the axe and its creation requires an unholy ritual involving both a fallen half-god and a lesser demon.
A Will-O-(The)-Wisp feeds on fear and can go invisible, so its typical behavior is to attack a party, disappear if it takes too much damage, stalk the party, and then attack again when it's least expected.
Dark Sun supplement Monstrous Compendium Appendix II: Terrors Beyond Tyr. Cilops are 15 foot long Creepy Centipedes that don't require any sleep and will track their prey (using both their sense of smell and psionics) for weeks without stopping.
Classic Traveller, Double Adventure "The Chamax Plague/Horde". The Chamax are incredibly determined to kill and eat. They have the ability to sense life at a distance and will travel great distances to obtain it. They can also sense radio broadcasts, which allows them to triangulate their victims' location at even longer distances.
While on the Frontier in Assassin's Creed III, you encounter wolves and bears which attack you on sight. Contrary to what happens in real life, the wolves are super persistent and attack you... even after you kill their alphas. They don't retreat even when it's in their best interest.
Alma from the Adventures of Lolo games. She'll normally mind her own business, but if Lolo should get within her field of vision, she'll roll after him until either she catches him or he takes refuge in a meadow.
Many of the monsters in Final Fantasy XII seem to go to rather crazy lengths to catch the party. The ones that teleport, however, won't leave you alone until you leave the room, and a few monsters might just keep going.
Several of the more mobile champions in League of Legends count as this, but Hecarim is the best. All of his abilities can be cast while moving, one greatly increases movement speed until a basic attack on an anemy, at which point he will launch both champions in his last move direction. His ultimate allows him to dravel through walls, trees, et cetera. You will never escape a Hecarim unless your team helps you.
There was a glitch in The Oregon Trail III that sometimes made wild animals act like this. If you went out hunting and fled from an angry bear, the bear would appear right in your face the next time you went hunting, ready to maul your party members. This bear would follow your wagon for thousands of miles until you managed to kill it.
While Peter Jackson's version of King Kong uses this trope full-force in the movie as seen above, and you still get chased way too far by the V. rexes, the Official Game Of The Movie actually averts this as a specific game mechanic. A lot of time, you can divert the attention of a predator away from you by killing something smaller, causing the larger enemy to take the easier meal. There are even giant dragonflies and grubs you can stab with a spear, specifically for creating such distractions.
The giant... black... troll... thing, from Castle Crashers. It just won't stop chasing you until it's dead, no matter how many arrows (or magic attacks) you throw at it.
The walrus chef in Crash Twinsanity, who chases you halfway across N Gin's battleship — over seemingly arbitrary holes in the floor, through walls of crates — even nitro crates don't slow it down.
Nemesis from Resident Evil 3: Nemesis deserves special mention as he can follow you even to other rooms. Normally all one had to do to run away from an enemy is go into another room, but you have to run away quite a bit from Nemesis before he finally gives up. It was explicitly engineered and programmed to hunt down S.T.A.R.S. members, which Jill is. That's all it was made to do.
Monster Hunter inverts this. Most large monsters tend to flee from the player after exhausting themselves or sustaining large amounts of damage, and usually have to be chased in order to be taken down. In other words, the player is the Super-Persistent Predator.
Limbo has the game's only boss, a giant spider. It has only one leg the last time it shows up, but despite that it still tries to kill you.
Justified in Vampire: The Masquerade - Bloodlines with the werewolves. Nines specifically decides to hide out in their territory because they're known to hate vampires, and no one will look for him there. Even then, they leave him alone, until a different vampire sets fire to their territory — then two of them go looking for retribution.
Metroid: Fusion has the SA-X, Samus' Power Suit taken over by an X-parasite which chases you through the entire game with no way to stop it. (The SA-X is fairly easy to fool, though, not being able to find Samus should she slip out of immediate view.)
On the other hand, since Metroids eat X-parasites, Samus effectively plays the role of Super Persistent Predator in the game itself.
Pokémon has Krookodile, a crook crocodilian that's said to never allow its prey to escape. Oddly, it doesn't learn the move Pursuit through normal means, though it's still better then Garchomp, who's said to be similarly persistent but doesn't learn the move at all.
While never specified to be a predator, Primeape fits the persistent part because it never gives up chasing whoever angers it till it has beaten them up. This happens a lot, because the Pokémon has such a extreme Hair-Trigger Temper it's near constantly in a Unstoppable Rage.
In gameplay, running away from a wild Pokemon is determined primarily by the difference in speed between the combatants. Fast wild Pokemon will simply not let you escape from battle.
Zig-Zagged in Metro2033. The Moscow mutants will go to great lengths for a meal, even going so far as to attack armored humans with automatic weapons. Similarly, they are not deterred by gunfire, bright light, or the smell of their own dead, as most normal animals. On the other hand, shooting them will usually cause them to back off momentarily, they do eventually flee if enough of their pack is killed, they are frightened of the anomalies and ghosts that infest the haunted tunnels, and they will also avoid large fires (though they will brave them if there is no other option). Totally averted with some other mutants — Librarians, the possibly-once-human, possibly sentient mutants that infest the Lenin Library and the Military Archives beneath it are simply territorial, and will even back down if you look them right in the eye (in the novel, one even tells Artyom to "go away" in Russian), and the Biomass under D6 ignores you until you start actively trying to kill it. The Demons, winged mutations of the tigers in the Moscow Zoo, will not try to follow you inside, though they will opportunistically try to snatch you if you spend too long outside or near windows. Overall, the unusual persistence of the Moscow predators is justified by the scarcity of food in the Metro — they are just as starved as the humans they feed on, and they really can't afford to ignore such a tempting target as an adult human (or better yet, woman and children he's guarding) unless they have no other option.
Last Light expands a bit on the situation, giving some of the mutants additional motivations for their behaviour and pushing the game closer to a full aversion of the trope. Watchmen are shown to possess a limited capacity for restraint and rational thought, being content to leave Artyom alone so long as they're not starving or if he doesn't provoke them. They are also more apt to break off an attack if they lose too many of their own, and the Baby Dark One points out that they fear what they don't understand when lending Artyom his psychic facilities to seek them out in cover with. On the other hand, Demons and the new Bear boss-mutant are both shown at various points in the game to be simply protecting their young, and the same is implied for the Nosalis Rhino (a Nosalis brood mother who watches over a large pack of them). The aquatic Shrimp are docile unless bothered by disturbances in the water, which a group of Reds promptly create while carelessly boating through Shrimp-infested tunnels.
In The Elder Scrolls IV: Oblivion, every enemy is this. That mountain lion, that wolf, that troll, that rat will chase you down to the ends of the earth in order to maul/feast upon your flesh. They will come after you through villages, forests, rivers, lakes, mountains, and plains, from the farthest western point of the map to to the farthest eastern point, in an all-consuming, single-minded drive to wreak vengeance on you for entering their line of sight.
The King of Miscarcand (a powerful undead boss fought in the main questline) has the trademark persistence of an Oblivion enemy, but (due to a bug) he never loses track of the player's position, and he's not afraid of entering crowded cities.
The Spotty Bulbears in Pikmin were already Demonic Spiders on their own, but Pikmin 2 upgraded them in numerous ways, one of which is that, while every other enemy in the game (except the similarly persistent but less threatening Gatling Groinks) has a set radius they'll stay in before giving up chasing you, they have no such limit and will follow you to the ends of the earth until one of you is dead. Even then, the Bulbear's corpse will have to be harvested, or it will come back to life.
Etrian Odyssey: Once you've triggered an F.O.E. encounter, you pretty much won't get rid of it until you kill it or it wipes your party.
Some F.O.E.'s are also programmed to start coming after your party as soon as you step foot into a dungeon, even if you haven't encountered it.
The T. Rex in Dino Crisis constantly hounds Regina throughout the entire game in a very similar manner to the Nemesis in Resident Evil 3.
In Telltale's Jurassic Park video game, the T-rex will constantly attack the protagonists throughout the game despite killing enough dinosaurs over the course of it that it REALLY has no reason to. The only thing that can distract it from chasing them is a Triceratops trying to kill it, and even then, it still takes a moment to divert its attention from the Triceratops to attack the humans.
In the Sega GenesisJurassic Park game, you can play as a Velociraptor whose sole motivation is to eat Dr. Grant. Each level the raptor is following his scent, going through the same levels you'd go through playing as Dr. Grant. She could eat the hundreds of dinosaurs and armed guards she kills trying to get to Grant, but no. Maybe the raptor has a thing against paleontologists.
In the Chimera Laboratory in Mother 3, the Ultimate Chimera is chasing you around. It can't be hurt, and if you touch it you'll get an instant game over without even entering battle. What's more, in New Pork City later on, you find it an inch from your face, SITTING ON A TOILET in a stall you just opened in the bathroom dungeon.
The player in Miasmata is being stalked by a deadly creature that will follow him around the entire island and is liable to attack at any hour of day or night.
Any regenerating Necromorph in Dead Space. They will hunt you, they are invincible and thus walking bullet sponges, their slow but unstoppable approach makes the player nervous, and they tend to be encountered in rooms with timed lockdown. Fortunately, you can get rid of them, just not so easily. Hunter, Übermorph, and Regenerators are stopped by shuttle engine, outrunning, and blasting to pieces, respectively.
In Gothic3, you will often encounter packs of animals in the wilderness, from large birds to wolves, rhinos, and other beasts. Without exception, as soon as you attack a member of the pack, the entire group will go into berserk attack mode and chase you to the ends of the earth until either you or they are dead. One upside of this is that you can lead them into populated areas like cities, where the guards will assist you in taking them down.
Most enemies in Final Fantasy XIV will give up chasing you after you run away for a while. Played straight in dungeons where enemies that spot you will hunt you down no matter how much you try to escape.
In Contagion, the Riot zombie is a zombie clad in bulletproof armor. It soaks up bullets like a sponge does water, and it is ridiculously persistent, chasing survivors throughout the entire map until it (the pursuer) is killed. They can be extremely difficult to deal with in harder difficulties where ammo is limited and zombies can kill in a minimal number of hits. The only easy way to get rid of it is to blow it up with an explosive weapon.
Tarvek: Oh, come on! What's wrong with this monster? Some of these people look delicious!
Unlike most other examples here, in Off-White the Super-Persistent Predator is a main character, though we probably aren't supposed to sympathize with his actions. Said character, the wolf Raigho, doesn't stop attacking the human Seven after he misunderstands and thinks she is impersonating a god like figure. Even after she gorges out his eye.
A rather terrifying example, the SCP Foundation features SCP-096, a normally harmless creature until you see its face. It then flies into a rage and will stop at nothing to kill you. Military-grade armaments have little to no effect during its pursuit of a target. The effect also works on pictures, and its face could be as small as four pixels and it would still make all attempts to brutally [DATA EXPUNGED]. And once you see its face it knows where you are, so looking at its picture while hundreds of miles away won't help you.
Naturally, the Foundation tried to kill 682 with it. It ended with both of them severely injured and leaving SCP-096 so afraid of 682 that it hides its own face in fear.
Poor old Wile E. Coyote, chasing the Roadrunner far beyond the call for reason, going so far as to buy countless Acme products and mountains of birdseed instead of spending that money on something he could actually eat. It actually was explained by Wile E. himself, in the only episode in which he speaks. He addresses the question of, "Why would a supposedly intelligent predator invest so much time and energy chasing a difficult prey with very little meat?" He shows a diagram of the roadrunner and how its different cuts correspond, in the coyote's palate, to the most sumptuous delicacies that humans enjoy.
One of the Rules for the Coyote and Roadrunner cartoons set in place by Chuck Jones, the rules that made the cartoons so awesome, is that "The Coyote can give up at any time." Being a Super-Persistent Predator is a choice of his own, maybe even an addiction he just can't quit, no matter what he does. Which is morbidly hilarious.
Tom of Tom and Jerry, whose obsession is best relayed through the fact that he once chased Jerry into a dog pound.
This is mostly Justified as Tom chases Jerry less out of hunger and more out of a desire to get even. Even when Tom's original intention was eating Jerry, he only really becomes persistent when Jerry sufficiently humiliates or injures him.
A Robot Chicken sketch involving The Smurfs getting killed in a flood has Gargamel, after years of trying to capture the Smurfs so he can eat them, finally being able to eat them (what with so many Smurf corpses). When he takes a bite though, the look on his face is that of "I've wasted my life". (In the original comics, he doesn't want to eat them (Azrael does), but use them as ingredients to create a philosopher's stone.)
The Garfield Show - A wolf chases after Jon, Odie, and Garfield riding in a car for twenty miles until it attacks them in their home. Justified because the wolf was a mother who wanted its baby, which Odie adopted and took with him after the picnic trip.
And the panther in the special Garfield in the Rough, which attacks them at their campsite and smashes the driver-side window of Jon's car with its head (taking two tries to break it), then turns to go after Garfield after he drops on its back and claws and bites the panther.
This trope is somewhat true of Sabor in The Legend of Tarzan; she only appears a couple of times, but both times she is incredibly single-minded about her chosen prey. If I were a leopard waiting to attack a baby and a gorilla showed up to protect it, I'd go find something easier; not Sabor.
To its most ludicrous extreme: In Kingdom Hearts, she repeatedly stalks and attacks a boy who can shoot fire and lightning from his body.
A panther in one episode of Timon & Pumbaa chased them into a tree, where the duo decided to wait for the predator to become disinterested and leave. They're frail, old men with canes and walkers by the time they decide to leave, and the equally-old and frail panther still wants to chase them!
The Goof Troop episode "Cabana Fever" features Pete going on vacation to a tropical island and running into a shark that's so determined to eat him that it climbs onto the land and chases him to a volcano.
Avatar: The Last Airbender: While both Zuko and Azula have followed the Gaang over ridiculous distances, Azula once chased them constantly for days, tracking them and then using a Fire Nation tank to follow them without having to stop for rest, leaving Aang and the others too exhausted to even set up camp. Finally facing a tired Avatar with no other option than to stand and fight, Azula likely would have won if not for the intervention of Zuko and Iroh.
Many predators really do behave this way, though not to the ridiculous extents often depicted in fiction (usually employed by a group of smaller predators pursuing one large prey animal, whereas many movies and TV shows have it reversed). The constant pursuit denies the prey a chance to feed, drink, or rest. Eventually the prey will either collapse or be too weak to defend itself. This can easily be sped up by injuring the prey or forcing them into dangerous terrain. These tactics can allow a slower, weaker predator to take down big game. The predator runs the same risks, so this can often be a make-it or break-it tactic.
Humans are perhaps the most successful example of this trope, called Persistence Hunting. We are nearly tireless by the standards of most other animals, though hardly fast animals — in our hunter-gatherer days, our favored tactic seems to have been following an animal at a jog until it simply dropped of exhaustion and heatstroke and either died there or had its head bashed in with a rock. This is still practiced by many African tribes (before you try it on your local whitetails, though, remember that these people are hunting in vast expanses of flat land; there's no forests for the animal to hide in or hills for it to vanish over.).
People often talk about humans as being slow and weak compared to other animals; however, in reality, our bipedal locomotion and long legs allow us to travel longer distances without rest than most other land animals, and our naked skin, upright posture, and watery sweat allow us to run even in hot weather where other animals would overheat, and humans know how to hunt in packs. So providing you are able to track your prey well (which humans can thanks to deductive reasoning and theory of mind), this is a pretty damn effective way of hunting.
The Tarahumara tribes of Northern Mexico have the Kalahari (the main African tribe that still hunts like this) beat. A common game for them is essentially a group race where teammates pass a ball to each other while running towards a general goal. The short races are a couple hours nonstop. The long races? A few days (and it's still nonstop, they walk for a break).
Humans are also this towards other humans. Give a human or group of humans enough of a motivating factor and they can pretty much chase down another human being almost endlessly, for years or decades, only giving up if they know the target human is dead or otherwise completely out of their reach. Popular example; Osama bin Laden. It took ten years for the United States to find him, but they eventually did catch and kill their prey.
Besides humans, there is another well-known pack animal which uses persistence as its primary hunting strategy: wolves. Kind of makes sense that these two species would have gotten along fairly well in ancient times, doesn't it? Man's Best Friend might have originated as a pack of wolves and a pack of humans getting to know each other while chasing down the same big game, teaming up to take it down, and sharing in the kill.
Speaking of canines, African wild dogs are persistent hunters. They will chase their prey until it tires out, sometimes for miles.
Hyenas are also known to do this.
This Killer Whale is certainly one. After chasing a dolphin for two hours, it made a four-meter-high jump to catch it. Other Orcas will drag whales and batter them until they can't fight back anymore and then drag it down to drown it.
Cracked.com's "The 5 Most Horrifying Bugs in the World" describes killer bees as follows (chemicals emitted by the detached stingers of the bees who already stung you attract the rest of the hive to continue the assault):
Regular bees will give you about nine seconds of being too close to the hive before deciding you're a threat and then attacking you. So it's pretty easy to just walk past them without any screams. And if you do get them after you, they'll consider you to be 'chased off' after about 300 feet. Africanized bees do not roll this way. They give you half a second of being too close before they decide it is time to completely fuck your shit up and empty the entire hive — tens, maybe hundreds of thousands of angry, angry bees. When you run, flailing and crying and soiling yourself while screaming "JESUS CHRIST I'M COVERED IN BEES," they will chase you for over half a mile.
Oh and if you do accidentally damage the hive of ANY type of bee and decide to escape by swimming, it doesn't work. The bees will wait for you to surface so they can fuck your day up. All those cartoons where the bees fly down the snorkel weren't exactly lying to you.
"The predator that won't stop chasing you" is an extremely common dream scenario— sometimes your brain isn't even courteous enough to show you WHAT is coming after you!
The Tsavo man-eaters, a pair of maneless Tsavo lions, killed/consumed between 35/135 Indian laborers working on the Tsavo railway bridge in British East Africa. Even lighting campfires and building redoubts out of thorns didn't stop them. Eventually, Col. John Henry Patterson, a real-life Great White Hunter, set off to kill them. He shot the first, but it escaped, then started stalking him. He shot it four more times, and it eventually died of its wounds. He found it lying dead in an ambush position where it had been waiting for him. He ambushed the second lion, shooting it five times. It got up and charged him. Three more bullets put it down. Patterson claimed it died trying to leap over a fallen tree branch, still trying to charge him.Then they spent 25 years as a rug.
These two were more recently turned into a museum exhibit (with one of them lying down, since the rug didn't include his belly). See the Movies entree for the movie based (somewhat loosely) on the event.
Gustave. What's scarier than an enormous Nile crocodile? An enormous Nile crocodile that not only has a taste for eating humans, but enjoys torturing them too. This bastard is reckoned to be nearly 70 years old, and, thanks to hundreds of human corpses dumped in the Rizizi river during Burundi's civil war, he has a taste for Homo sapiens. He is believed to have killed nearly 300 people, and according to locals, doesn't eat them all - he kills because he enjoys it. Also, this horrific abomination is still out there. A National Geographic expedition tried to capture him using a steel cage and a live goat. After the camera went out one stormy night, they found the cage the next morning, the goat gone, smashed to pieces at the bottom of a lakebed. So what makes him "super-persistent?" Well, apart form his enormous size, his other distinguishing features are machine gun scars, a grenade wound, and having an enormous bullet hole in the middle of his face.And he's still going...
Komodo Dragons fit the bill; they first take a bite out of their prey, and through a combination of mild anticoagulant venom (ie, the wound bleeds out) and bacteria-laden saliva, it's only a matter of time before the animal drops from blood loss and infection, while the dragon tracks from afar with its sense of smell.
Some paleontologists believe that large predatory dinosaurs, including the T-Rex, may have practiced this method of killing as well.
Various saber-toothed predatory mammals also, although in their case it was inflict-deep-gushing-slashes-and-wait, not inflict-infectious/toxic-bites-and-wait.
Great white sharks still use that strategy to prey on elephant seals.