Feeding people to monsters or man-eating animals is one of the classic perils that villains and others subject people to.
Sometimes this is a Human Sacrifice to a demon, dragon, Eldritch Abomination, or some other monster or beast. These scenarios usually have some poor unfortunate Chained to a Rock awaiting their doom. Maybe the local religion demands this to be done to Appease The Volcano God. Maybe the monster wants tribute in the form of people to eat, such as with many dragons. Maybe this is even meant as a punishment, in the case of Daniel in the lion's den from The Bible or Andromeda from Classical Mythology.
Other times, the beast is a Right-Hand Attack Dog — a pet or other creature that the villain keeps around for some reason, which he uses to dispose of victims, and more than one villain's underling has met their end in this way, usually after they've failed him or outlived their usefulness. If a villain tries to do this to the hero, expect the hero to kill the beast or escape in some other fashion. It's also not uncommon for villains fond of feeding people to beasts to meet their end by being eaten by the beastin turn, if the hero didn't kill the beast beforehand.
Fantasy villains have all kinds of monsters to choose from, ranging from dragons to giant snakes to giant vermin to demons or something even weirder. Contemporary and pulp villains will often have their victims eaten by tigers or sharks or some other large man-eating carnivore. Sci-fi villains will often have some really freaky alien monster to feed people to.
The Shark Pool and the Snake Pit are two quite common forms of this particular trope. Also related as Animal Assassin, a more clandestine way of killing people using animals.
See also Just Desserts and Eat Me.
Anime and Manga
Apostles in Berserk are fond of forcing their subjects to send them people to eat, such as the Baron of Koka Castle and the Count.
In addition, this is the intended result of sacrificing someone to the Godhand so that one can be reborn as a demon, with the person in question often being Eaten Alive.
In Fushigi Yuugi, the Priestess is technically a Virgin Sacrifice for the Beast God she summons. It also functions as a Secret Test of Character; if she uses her wishes for the good of others over herself and possesses enough strength of will, she can escape having her soul eaten. Out of the four priestesses, two (Miaka and Suzuno) escape. The third (Takiko) was dying already so Genbu started to eat her soul and her dad mercy killed her. The fourth (Yui) is fully devoured, but Miaka uses one of her wishes to bring her Back from the Dead.
Also, there was a snow-demon in the novel that explains Nuriko's backstory that demanded a more conventional Virgin Sacrifice from the village nearby. He eats Nuriko's companion.
In the Star Wars saga, Jabba the Hutt was quite fond of feeding people to a Rancor, including Twi'lek slave dancer Oola in a notorious Kick the Dog moment. He isn't quite so successful in his attempt to do the same to Luke.
And once he's short one Rancor, he tries it again with the Sarlacc.
The Geonosians actually did this with an Acklay (a semi-aquatic lobster-praying mantis hybrid), a Nexu (a porcupine-tiger hybrid with four eyes and two tails), and a Reek (a minotaurlike monster with three horns on its head).
Ratigan feeds a hapless lackey to his pet cat Felicia in The Great Mouse Detective. Weird, because the professor himself is a rodent.
In Goldmember, Dr Evil does get his Sharks with Frickin' Laser Beams on their heads and Mr Roboto is later fed to the sharks for his failure. However, a deleted scene shows that everyone in the vicinity(Even Dr Evil), couldn't hold their lunch over that scene.
Indeed, this trope is so often used to James Bond parodies it's one of the things thought to happen in Bond movies a lot more often than it actually does.
Licence To Kill. Sanchez badly maims Felix Leiter by having him thrown into a Shark Pool in revenge for his role in his capture as the rest of his men murder Della, Felix's new wife. Bond starts his Roaring Rampage of Revenge by feeding Killifer, the bribed DEA agent who helped to spring Sanchez, to the shark in turn.
In Skyfall Bond and a mook fall into a pit of Komodo dragons. The latter gets eaten by one of the lizards.
Conan's first dungeon crawl in Conan the Barbarian ends with him killing a big-ass snake that was supposed to eat a girl that the snake cult was going to sacrifice.
Shao Kahn disposes of Jade this way for failing to kill the heroes in Mortal Kombat: Annihilation, feeding her to a monster carving in a wall (and for extra Narm points, the carving gives out a great big burp after it's done with her).
In Dragonslayer, the king feeds virgins to the title dragon every year in order to appease it so it will leave his lands alone. The plot kicks off when Elspeth, the king's daughter, ends up on the menu.
M. Bison in the film of Street Fighter attempts to do this, proclaiming his idea to the would-be victims in (OF COURSE!) wonderfully hammy fashion. Blanka, the "beast" in question, has other ideas.
Humorously averted in Dragonheart, in which con-man knight Bowen attempts to rid himself of a nusiance rabble-rouser by suggesting to her village that dragons can be placated with virgin sacrifices. His dragon partner finds the idea ridiculous, and even expresses disgust at the idea of eating a human. Except when he must chew in self-defense (but he doesn't swallow).
In ''Peter Pan: Return to Neverland'', Captain Hook is actually revealed to have a pet octopus in which he will often feed unsuspecting pirates to if they disobey him. However, near the end of the film, said octopus eventually develops an obsession of eating Captain Hook as well, and as a result he actually starts to frighten the pirate by constanly bobbing its eyes upside down like you-know-who.
Following the Christian Martyrology claims (see below), many oldschool films set in Ancient Rome include representations of Christians condemned to this. The film version of Quo Vadis has a bunch of Christian kids forced to put on sheep skins before they had a hungry lion released on them; it was such a Kick the Dog moment that the spectators were horrified (and mind you, these were all pagans who hated Christianity), and when Gentle Giant Ursui pulled a Big Damn Heroes for them, the audience pleaded with Nero to give Ursus a thumbs-up.
In Robert E. Howard's "The Scarlet Citadel," Tsotha imprisons Conan the Barbarian in the dungeons below the title citadel, with the intent of having him be eaten by Satha, another big-ass snake. The snake ends up killing a slave of Tsotha's who was planning to kill Conan in revenge for his brother's death during Conan's pirate days, when he was called Amra.
Has happened to Alex Rider at least once in his career.
In the Harry Potter books, Voldemort generally feeds his victims to his snake, Nagini, although they're usually (if not always) dead first.
Well of course they're usually dead. He doesn't want them hurting his snake by struggling, after all. Especially since the snake is a Soul Jar.
Animorphs had a unique variant of this. A Yeerk who had displeased the Visser one too many times was fed to a natural Yeerk predator nicknamed the Yeerkbane. I believe Vanarx was the actual name. It enveloped the host's head with its mouth and sucked the Yeerk right out of the host's head. Yikes.
He also enjoys feeding them to the Taxxons as well.
In the short story 'Sandkings' by George R. R. Martin the main character gets into the habit of feeding people to his new pets, the eponymous insect-like alien monsters.
Notably, this short story was later (very) loosely adapted into the pilot episode of the 1995 relaunch of The Outer Limits TV series.
The first book of Galaxy of Fear has the planet itselfkilling and consuming people so quickly that they don't suffer. The heroes manage to piss off the Enzeen enough that they carried them to the "heart" of D'vouran, where being eaten would be far slower and more painful.
In the second book the Big Bad tells his lackey to listen carefully or be fed to his battle dogs.
Saint George is famous for slaying a dragon that did have a taste for villagers, in particular young women.
Older Than Feudalism: The Bible has the story of Daniel, who was thrown into a lion's den due to a law that some princes had tricked King Darius, who liked Daniel, into passing because they were jealous of his faith and hard work. Daniel, who has always been faithful to the Lord, was protected by one of God's angels, who shut the mouths of the lions. When the king learned that Daniel was still alive after spending the entire night in the den, he had Daniel taken out of the lion's den and the princes and their families thrown in instead, where they promptly got eaten by the lions.
Christians in Roman times were supposedly fed to lions in the arena as well. At least, that's the excuse one Pope used for declaring the Colosseum a monument to martyrs to protect it from commercial development. The historical truth of that claim is more murky.
Damnatio ad bestias was the usual Roman punishment of particularly vicious murderers and those convicted from high treason.
According to legend, St. Margaret was sentenced to be fed to a dragon. Large constrictor snakes, such as African rock python, are known to be able to smother and devour large prey - occassionally children and youngsters. They also often were referred as "dragons". The Romans knew the rock python, and if Margaret was a petite lady and the snake had been a large specimen, the legend may well be plausible.
In Japanese Mythology, the Yamata no Orochi was an eight-headed and eight-tailed monster that forced a pair of earthly deities to hand over one of their daughters to be devoured by the beast every year. Their eighth and final daughter, Princess Kushinada, was saved from this fate by the storm god Susano-o, who slew the beast by impersonating her, getting it drunk on eight large bowls of sake, and then chopping off each of its eight heads.
Players of Dwarf Fortress frequently build pits containing large and vile-tempered captured creatures. Sometimes these are trained, sometimes they're not. Crocodiles, zombies, wolves...people even build giant cave spider pits, and harvest the web left after a successful termination.
In Drakensang 2: The River of Time, the vile commander of Thurstone Fortress Stitus Bloomfold (thinks of a midget version of Dom De Luise) has a taste for rare pets, which he feeds with hapless prisoners from time to time. Said critters include war hounds, wild boars, wolves and a bear. Later he tries to feed the party to his favourite beastie, a Newt Kraken, but ends up suffering a Karmic Death instead, as Forgrimm lampshades.
In The Pirates of Dark Water, Bloth has a vicious monster called the Constrictus he keeps in a pool of water in his ship. Failing to fulfil his tasks (Or being someone he doesn't like) is a good way to get dumped into it. The only survivors of this fate are Ren and Konk, and the latter lost his leg doing so.
The snake-obsessed Kobra organization in Batman Beyond uses a variant of this. Any member who fails their duties, or anyone else who knows too much about their operations, is dropped into a pit of venomous snakes where they are presumably bitten to death.
Chairface Chippendale in The Tick tries to feed the heroes to his pit of man-eating alligators.