Ms. Goldenweek in the manga of One Piece was last seen being pounced on by a giant riding duck and not seen again until about 250 chapters later in a mini-arc.
In Princess Mononoke, Eboshi is finally taken out by the decapitated head of the giant wolf spirit she just fatally shot. While she survives having her entire arm bitten off, she won't be using any of the guns her factory produced again.
In A Bug's Life, the ants discover that main villain Hopper is afraid of birds, so they build a fake one to try and scare him away. He sees right through their ploy; so when Flik and Princess Atta lead him to an ACTUAL bird in the finale, he doesn't realize it's not a trick until it's too late.
Captain Hook, from Disney's original film of Peter Pan, exits pursued by the crocodile. Depending on which sequel you go by (the animated sequel or Hook), it may have gone badly for the crocodile.
If you go by the animated sequel (Return to Neverland), this happens again when an octopus sees Hook and his entire crew as codfish, and pursuits them all.
Big Boss in Rio 2 gets swallowed by a boa constrictor.
Scar in The Lion King finds his end by the hyenas. Particularly chilling, since most other examples of this trope treats the animal as the vessel for Karma, or just a force of nature. But the hyenas that eat Scar were goofy, well-characterized villains earlier in the film, making his death feel like a murder rather than an accident.
Film - Live-Action
The literal phrase was used by the young high school gang when they left in The World's End, but morphed into "Let's Boo Boo!"
In the Nicolas Cage/Samuel L. Jackson film Amos & Andrew, the bloodhounds from earlier in the movie go chasing after the police chief near the end.
In The Naked Gun 2 1/2, Robert Goulet's character survives a fall from a building unscathed, only to be mauled by a lion seconds later.
The climax from Ace Ventura: When Nature Calls seems to imply the villain is not so much pursued by the gorilla as pursued by it.
In Kenneth Oppel's novel Airborn, Szpirglas, the infamous Sky Pirate, is killed, not by the main character, Matt Cruse, but by a pride of the huge, flying, predatory felines aptly named 'Cloud Cats'. Interestingly, despite pursuing some of the protagonists, the Cloud Cats never seriously injured any of the "Good Guys".
In the Doc Savage story Fortress of Solitude, the escaping John Sunlight is followed to a point where his tracks meet those of a polar bear next to an open lead in the ice. Since there's a lot of blood and no tracks leading away, they draw the obvious (and incorrect) conclusion.
The ghost of Shakespeare himself appears and invokes this trope in Grailblazers. As a literal ghost writer for the British soap Coronation Street, he ends one scene in his script with "Exit Ken Barlow, pursued by a bear."
At the end of Harry Potter and the Order of the Phoenix, Umbridge is captured and carried away by a herd of centaurs. Dumbledore somehow persuades them to let her go between chapters, and she turns up in the hospital wing relatively unharmed, though she jumps if someone mimics the sound of hooves. (What exactly happened to her while in their custody is never revealed, though the usual suspects put forward their own theories.) When she tries to sneak out of the castle, Peeves catches on and she ends up exiting, Pursued by a Poltergeist with a Walking Stick.
In the Sister Mary Helen mystery Death of an Angel, the B plot covers an alumna's plan to murderher domeineering, abusive mother. Her plan for disposing of the body is to underfeed her mother's standard poodles, and then set them on the dead body so that there will be nothing to implicate her. However, in the confrontation, Mama injures her face. Then the rapist-murderer from the A plot invades the house, and then the two nuns who are the amateur sleuths in the series arrive, as do the police. The rapist is stopped but then dogs come from the basement and smell the blood on Angelica's face and attack her. Inspector Gallegher shoots them dead, but Angelica is mortally wounded and succumbs to her injuries the next morning.
In The Cat Who Said Cheese, an abusive ex-husband tracks his ex-wife to Moose County, using the fact that back in the navy he saved a shipmate's life (said shipmate still suffered brain damag)e as leverage to coerce the local, now a beekeeper into becoming an accessory to the bombing of said frightened ex's hotel room. When he comes back to try and cover his tracks and finish the job—the intended target was out and about but someone else died—the beekeeper inadvertently gives him a wool blanket and the bees swarm the murderer, who is found dead the next morning.
In the Live and Let Die novel, Mr. Big tries to feed James Bond and Solitaire to sharks and barracudas, by dragging them behind his boat. However, the bomb Bond had planted in the boat detonates, and Mr. Big falls in the water, to be eaten by the sharks and barracudas himself.
In "The Zeppo", the villain is making a speech about how he will be coming back, when he opens a door on Werewolf Oz. He is not seen again, and in the next scene Human Oz remarks that he feels full for some reason.
In "The Pack", the evil zookeeper ends up being eaten by hyenas after Buffy hurls him into the hyena pit. Knowing her, she probably didn't mean for him to end up in the pit, but she doesn't shed any tears about it later.
In the Good Eats episode about dried fruit, Alton offers his homemade trail mix to two hikers, then warns them to run. The hikers are chased off by a guy in a bear suit.
Carcassonne: In variation Carcassonne: Hunters and Gatherers, meadows contain deer, aurochs, and mammoths that contribute to the scoring. However, each tiger devours one deer, and negates the points.
The Older Than SteamTrope Namer is Antigonus from William Shakespeare's The Winter's Tale. Though not truly the villain, he is dispatched in this manner. (And unlike most of the other examples on this page, the bear literally comes out ofnowhere just for this scene.)note A side note: there was a popular bear-baiting ring right next to the Globe theater where Shakespeare worked, so it's possible that he (or his producer) randomly decided to borrow a bear for a crowd-pleasing cameo. (Though one can imagine the villain might not have been the only individual pursued by a bear in that event.)
A stage show by Ishmael Skyes, playing one of Shakespeare's actors, narrated an incident where he couldn't see out of the bear costume, leading to the memorable line:
Exit a bear, led by Antigonus.
Lucius Malfoy gets attacked by Werewolf!Lupin and dragged into the Forbidden Forest in A Very Potter Sequel.
In Paper Mario, Chapter 2's boss, Tutankoopa, exits pursued by his pet Chain Chomp.
An In-Universe example can be found in a fairy tale book in Drakensang: in the tale, a jerkass kraken keeps all the treasure from a sunken ship for himself, and won't share it with his friends. Later, a massive Water Dragon arrives (enticed by the Kraken's treasure) and chase him "so far away that noone ever saw him again".
One Where on Earth Is Carmen Sandiego? episode has Zack and Ivy chased by jaguars in a Mayan temple before running into VILE henchmen. The bad guys ended up at the bottom of a pit with the jaguars drawing near.
In an episode of Garfield and Friends, Garfield is working on a movie as a stunt cat and put in several dangerous stunts. Garfield looks through the script to see what's next and finds out it involves him apparently being mauled by a bear. Garfield pours honey on the director's chair and when he sits down he gets stuck. The bear is attracted by the honey and chases the director who has to hop off set.