If my information state s includes the possibility that the dog belongs to Bob and is male, then s[B→F] = ∅.

This is true only if "dog belongs to Bob and is male" is the only (kind of) possibility in your initial information state, which is different from the situation I described. In my example, you don't have to "get back to" the possibilities that the dog is female or belongs to Alice; you never lost them.

If you're specifically interested unsuccessful updates, I'm not personally aware of any built-in rules for belief revision in dynamic semantics. Belief revision itself is also an active but distinct area of research. If an update could never be successful (like "If it's a dog, then it's not a dog"), then you can dismiss it as absurd or unassertable without revising your beliefs.