Wonko-san,
...ja nai ka (dewa arimasen ka) = isn't it, aren't they, don't they, can't you, doesn't it, etc. In other words, a question asked negatively (almost as a rhetorical sometimes). I wouldn't really call this a negative question that implies a level of politeness. More of a stylistic, even stronger, way of asking a negative. I'd defer to a native, though, if they have a different take.
Ex.
Person 1: Anata, sakana ga kirai deshou? (You don't like fish, right?)
Person 2: Nani wo iu? Ima sushi wo tabete iru ja nai desu ka. (What are saying? I'm eating sushi right now, aren't I?)
Ex.
Hen na nioi ga suru ja nai? ("You can smell that (bad smell), can't you?" or "It smells off, doesn't it?")