** Using WeBWorK **

I sort of remember that a negative score for a problmem has special meaning somehow, but I can't seem to find it in the code anywhere, so I may be misremembering it.

You would probably need to write your own grader for this, as the standard ones only set the problem's score if the score on the current attempt is greater than the recorded score, which I think defaults to 0. That means that although an attempt might yield a negative score, it would never be saved. The grader is the place where this is done, and you could return a negative score there if you wanted, but you would need to be careful about the logic; in particular, how to treat scores of zero (like when no answers have been given, or no previous answers have been recorded) so that the student can't prevent the negative score by simply submitting all blank answers (getting a score of 0).

Davide