I'm confused - not difficult!!
Is this critter coming into your house or into a yard area?
I don't leave any uneaten food outside - though no chance of that with my two piggies but raccoons, foxes, rats, possums etc will all come for a snack.
Maybe your dogs don't see whatever it is a threat so they don't bark, they can get used to things that they see around a lot
My other thought is a snake of some sort, if they're hungry or lazy hunters they'll eat anything I imagine and so quiet a sleeping dog(s) might not notice.