Come Back, My Pet

An owner and their pet have a falling out, where the owner either replaces the pet or shoos it away. Then circumstances happen where the owner needs their pet back or is in danger, and only their pet can rescue them. They reconcile, and the statue quo is returned. This is not limited to standard pets like dogs or cats, by the way; even a tiny creature like a termite can fit the bill if they are treated like a pet -- that is, cared for and nurtured, with a genuine bond.

Compare with Timmy in a Well, when the pet and owner weren't separated before the human gets into trouble; Androcles' Lion, where the animal isn't a pet and they weren't together to begin with; and Tropey Come Home, where the separation is involuntary.

Anime and Manga

 * In an early Sailor Moon episode, the Monster of the Week attempts to do this indirectly by brainwashing the ailurophobic Shingo with an energy-stealing pet, just as Usagi is trying to convince her family to adopt her new cat and mentor, Luna. Usagi herself nearly gets brainwashed...but Luna scratches her to snap her out of it. Later Sailor Moon frees Shingo and other humans from brainwashing; as Shingo asks how he can return the favor, Sailor Moon advises him to be nice to cats. The episode ends with Shingo feeding Luna, and making peace with her.

Comic Books

 * A Goof Troop comic in which Pete replaces his dog with a cardboard robot guard dog after their house gets robbed. Turns out "Card" is actually programmed to let its creator inside to rob the house again.
 * A sad subversion is in the graphic novel Housecat Trouble. The cat duo that hunts down ghosts explains to Buster the kitten that their owners have actually been looking for them after a house-fire. The humans have been terrified Nova and Chauncey were killed or are lost in the streets and doesn't blame them for what happened. Nova and Chauncey say they can't return because hauntings caused the fires, and it was their responsibility to protect their humans. So they travel to help other cats learn to fight ghosts, and defend their home turf.

Film

 * In Lilo & Stitch, Lilo hits her Rage Breaking Point and tells Stitch to go away after she discovers that he's an alien, and that he's the reason that they were being pursued by Jumba and Pleakley. Right after, however, she gets captured by Gantu, and Stitch rescues her. Lilo during this juncture is more worried for Stitch than herself since Gantu tosses him off his ship and tries shooting him at point-blank range. She screams for him to wake up after he's briefly dazed and nearly immolated.
 * One of the most dramatic examples is in St. Bernard Beethoven films where the Big Bad, an evil veterinarian that does unethical animal experiments, goads Beethoven into pouncing on him by smacking him after smearing them both with red paint, to fake an arm injury. Though little Emily witnessed this and tells her parents that "He hit Beethoven!", her dad decides to follow the vet's instructions and take Beethoven to be euthanized, against even his wife's wishes who wants to figure out exactly what happened. When he comes home, they give him the cold shoulder with Emily calling him a "dog-killer" and his wife being extremely disappointed. Realizing that he made a big mistake, the dad drives them to pick up Beethoven and say he believes his daughter. They then realized that he really made a mistake when they notice the vet's arm is perfectly fine and the man lies that he euthanized Beethoven already. Cue the climax of the movie.

Live-Action TV

 * Joe did this by accident in Wishbone while testing out a new bike. He saved up all his money for it and doesn't want Wishbone to touch it. Wishbone is also too small to catch up with the bike while Joe is test-riding it, so Joe ties him to a tree on the path and orders him to stay. Wishbone is not about that; he slips out of his leash-- and license collar-- to play with a Golden Retriever and gets lost. A widower named Hubert saves Wishbone from a ditch and takes him in for the night, hoping to find "Spot"'s owner in the morning while talking fondly about his late wife, and how she loved dogs. Joe gets Adult Fear when he finds the empty collar, unable to sleep that night and preparing to spend the next day papering the town with Lost Dog signs. He hears Wishbone barking in the woods, finding him -- and Hubert-- at the same ditch where Wishbone fell the day before. Hubert is relieved that he found the dog's owner and real name, while Joe sincerely thanks him for saving Wishbone's life. They all strike a compromise: the episode ends with Hubert spending time with Wishbone while Joe goes out riding with his friends.
 * The hellhound in Good Omens is supposed to identify the Antichrist and follow him blindly. Adam, however, says he wants an ordinary mixed-breed named Dog, and the hellhound changes accordingly. As the day goes on, Dog becomes less demonic and more ordinary. When Adam's powers awaken and he scares his friends while talking about his plans for the universe, he lets them leave after they start crying, but takes offense when Dog goes with them. He chases them down, accusing his friends of stealing Dog. Pepper snaps at Adam that he's scared his friends away, and Dog doesn't want to be with him while he's being a power-hungry jerk. This realization brings Adam back to his senses; he goes from floating in the sky with storm clouds to collapsing on the ground, crying. Dog as a result comes back, as do his friends, and cuddles him. Slowly, Adam revives and realizes he has a new purpose: to stop the apocalypse. But he needs their help.

Literature

 * In the Hans Christian Andersen tale "The Nightingale", the Emperor of China tames a nightingale, but neglects it in favor of a clockwork bird. When Death comes for the Emperor, it is the live Nightingale who charms the Grim Reaper with his sweet song.
 * In The Hunger Games, Katniss and Buttercup the cat have hated each other from the day that Prim adopted him. To Katniss, he's another mouth to feed, and to Buttercup, Katniss is a disagreeable human. Then the end of book three happens, where.

Western Animation

 * Courage the Cowardly Dog: Courage routinely does this for Eustace, who routinely scares and abuses him. However, it's less out of the goodness of his heart and more because of his devotion for Eustace's wife Muriel.
 * In a Tom and Jerry cartoon, Tom's owner gets annoyed that Tom never tries to catch Jerry anymore so replaces him with a robot mouse catcher and Tom is kicked out. Since Jerry can't live in the house due to the robot throwing him out he and Tom work together and eventually the robot goes wild and Tom rescues his owner.
 * In Dexter's Laboratory, Dexter had this happen with his termite Timmy. Timmy is raised to eat up all the mess that Deedee creates. One day, however, Deedee is unusually neat and Timmy is hungry and lonely when Dexter has to leave so he eats up several important machines. Dexter banishes him, only to find his lab deluged with Deedee damage and goes searching for Timmy. They reach a compromise where Timmy raises a family of termites, giving him a support system.
 * Inverted in an episode of The Owl House where, as part of a bet with Eda the Owl Lady, the dog-like demon King makes her live in the outlier shed while training his "son", a giant garbage worm. He comes and begs for her help when "King Jr." grows out of control and eats up all his treats. Eda is more than happy to assist, and teasing him by calling King "Mr. Wiggles" as she threatened to if she won the bet.
 * Family Guy parodied this when Peter brings home "new Brian" after his Brian is revealed to be too old to save Peter from stupid stunts. Feeling crowded out and reminded of his age, Brian goes to live with Cleveland, preferring the indignities of being on a leash to being taken for granted. Stewie can't stand how happy and oblivious new Brian is, and tries to kick him out. New Brian responds by implying he used Stewie's teddy bear to masturbate. Cut to Stewie disposing of a bloody garbage bag, and the Griffins reading an obviously-fake suicide note. Brian is welcomed back, and he consents to Peter cuddling with a hamster that appeared out of nowhere.