Well, I think the non-aggression principle applies without reference to the 'justice system'. That is to say, whether or not someone has committed a crime, for which they may or may not have been convicted, they have a moral obligation not to perpetrate violence against you. Post-hoc detention or punishment does not 'correct' or remediate aggression, and I am not aware of any right to prevent hypothetical aggression.

I guess we're going off on a tangent here, but then I'm not sure what a person's right to freedom from violent crime actually provides them, if not a systematic process by which they can get justice.

I don't think there is a real "right to freedom from violent crime", at least not in the enforceable sense.

I would say there is a moral duty not to commit violence against others, and there is a moral right to defend one's self, but I don't see how you really guarantee "right to freedom from violent crime", so it really seems more like a dubious promise. This may be a consequence of my general skepticism of positive rights.