It happens randomly, when I get in back to a world where I have my animals such as horses, parrots, wolves. I'm not certain in villagers and other mobs but tameable mobs surely do.

The steps to replicate this could be:

1. Create a survival new world.
2. Tame some animals.
3. Log out the world.
4. Log in again.

Not all time that one logs in back the mobs would despawn but it is very likely to happen.