Lost Pets
The term of lost pets refers to animals or mobs that were at some point tamed or owned by an individual who has since abandonned them. This can happen either when a player becomes inactive, moves away or more commonly when they die. Lost pets can mainly be found near spawn with dogs being the most frequently found pet.
Context
A few animals in Minecraft are directly tied to the person that has tamed them with no way to be untamed or given to another player. These include cats, dogs and parrots. As such, when the original owners of these pets go missing, they become stuck, sat for eternity.
However, lost pets also include animals that aren't directly tied to an owner but that can still be tamed. This category includes horses, donkeys, mules, camels and llamas. Although these animals aren't stuck, they have still been abandonned by their original owner.
Freeing pets
When talking about "freeing" pets that have been abandonned, the most common solution among players is to simply kill them. However, this can be problematic as it is complicated to find the original owner of lost pets, leaving a certain margin of uncertainty as to whether a pet is truly abandonned or not. As a result, most players simply let these lost pets alone, in the hopes that their owner is not dead and eventually coming back to get them.
More recently, somewhere around the 3rd of October, a player named BloodyOrphan decided to create Doggy Heaven, a sanctuary in the sky where atleast 10 lost dogs have found a new home. His services have been used by dead and inactive players alike to give a final resting place to their pets.