Is it possible for flies to feed on rotting wood?

I live in an apartment that has recently become infested with flies and their larva and pupa. About once a week we find them crawling all over the carpet. They seem to be especially concentrated around the parameter of the apartment- where the wall meets the carpet. We cannot figure out where the maggots are coming from. Is it possible that they could be attracted to rotting wood that could be below the carpet? We don't have any rotting food or feces laying around, naturally. Any insight would be helpful!