Where does it go?

There is no universal trash. If the ad was a web link and you close it you can go to your web history and reopen it. If you receive a photo and delete it you can recover it from the recently deleted album. Offhand I can’t think of anything else that might be airdropped. A pdf maybe, a word processor file, in general they can’t be recovered.

That depends on the type of content airdropped, and whether the app that received it has a way to recover deleted items.