How do you handle the "No" man?

I've been doing some thinking about anarcho-capitalism and I would like to get some outside insight on this.

How do you handle the "No" man? Following the NAP to it's logical end doesn't account for the man that says "No." My thought experiment truncates to this: Person A steals $100 dollars from Person B. Person B seeks damages from Person A. Verdict is delivered, Person A is guilty. Sentence is delivered. Person A says "I will not accept that" and walks out of the court room.
My understanding of the NAP is such that as long as I am not acting aggressively towards anyone at that moment, they cannot act with aggression towards me. What would stop me from walking out of that court room?