My aunt's dog had the same affliction for a long time! She ate everything and would destroy anything that stood between her and some potential food. But she only lost weight, lost all of her hair and started breaking out in sores.
Eventually one vet started treating her for every worm/parasite he could think of, and they kept treating her for 6 months or longer. She is now fine.
I hope you guys find out what is wrong! Take care
Always so scary.