One time, my sister and I had gone on a journey to a jungle to get cats and parrots, and when we had finally brought them all back home (but my sister hadn't yet told the animals to sit down), my dad had told me I had to do something so I closed the LAN game, but when we came back and my sister logged back in, her cats and parrots were gone, nowhere to be found. Of course, I had to go to the jungle again to get at least 1 cats to protect her from creepers, but parrots can't be bred back, so although I found one parrot for her, she had many fewer than from her several hour long collection that disappeared. 

Later on, when I journeyed in a completely other direction to find an ocean monument, I suppose I had luckily and randomly loaded in a chunk which contained my sister's cats and parrots, because all of a sudden my sister was surrounded with (her) cats and parrots in her house. They had teleported back to her.

I don't know why these animals teleported to this random chunk on closing the world.