"Perhaps, some bird lives in there" or "perhaps, a bird lives in there?"
Solution 1:
I would probably use a in this sentence, but you could use either.
One of the meanings of some is:
some 2 used to refer to someone or something that is unknown or unspecified : she married some newspaper magnate twice her age | there must be some mistake | he's in some kind of trouble.
So to refer to "some bird" living in a tree trunk simply means it is an unknown or unspecified bird, if it does in fact exist. But the indefinite article accomplishes the same task, and does so with a single letter, so I would prefer it in this case.