Can you use the Annihilation card on a Giant Skunk that someone else is fighting?
If the Giant Skunk has just been played (via Kicking Down The Door or Looking For Trouble), then you may play Annihilation to cancel the Giant Skunk. At the time it's being played, it doesn't have all of its defensive text; Annihilation means it never existed.

Once it's in play, Annihilation won't help, because that isn't a monster enhancer or wandering monster.

So if you're going to Annihilate a Giant Skunk, be quick about it.

Source: Steve Jackson Games Forum