Ideas
I just ran into the same problem: after the fair ended, the lama disappeared. Moreover, my family won the first place for her, the prize was received, but the lama did not return. Lama disappeared even from the relationship panel, so she actually disappeared. I can't send a private message to EA_Solaire, there's just no send private message button, but I want to provide the save files via Google Drive.
There are also related problems with fairs:
1) they don't end on time. In the calendar, the end time is 21:30, in fact, the fair ends in an hour, at 22:30. But the last fair where my llama disappeared ended at ~00:10. Maybe it's because the fair overlapped with the New Year holiday?
2) When you submit an animal to a competition (I tested it with a cow and a lama), the animal does not leave the barn. But when you click on the barn, a bar appears that "your sim has already applied for participation." At the same time, the animal that brought by NPC comes out of the stable and is available for all actions (to chat, pet, etc.)
There are only minor mods in my game (changing names when generating Sims and replacing city backgrounds). And maybe it's not a matter of mods, because the cow from the last fair successfully returned in the luggage with my family, that is, the mistake is kind of random.