Assessing students in exams with negative points?
Grade that goes below zero doesn't make sense.


What makes you say that?  In some real-world scenarios, thinking you know the answer and being wrong is worse than realizing you don't know.  For example, I'd rather have my doctor or lawyer recognize when something goes beyond their expertise, so I can consult a specialist rather than following mistaken advice.  I imagine the same is true for most professionals, such as engineers.

If not answering at all yields a grade of zero, then it's reasonable to award negative points for a truly bad answer.  (Of course an insightful but flawed answer may still deserve a positive score, just not as high as the correct answer.)

In practice the most common case I've seen negative scores used is multiple choice exams, for the reason given by GeneMachine, but one can make a philosophical case for applying them much more broadly.