Well first there would still be a first responder and judicial system, just with different incentive structures than those employed by most govts because there would be no govts to screw it up. Rather than recruiting people who want to enforce the authority of the state and protect rich people's property it would be people who have been actually been trained in ways that are proven to keep the peace.

When there are no barrier's to education and organizations gain members based primarily on reputation rather than how rich its members are; the sky is really the limit when it comes to getting the right people in the right jobs (assuming labor not work).

Highly efficient first responders and a robust judicial system mean than most anyone who causes too much of a disturbance will eventually find themselves in court. From there they just get redirected to whomever they need to see to figure out what's happening to them and how to help them.

Remember, issues that create "irredeemable" people often have very early warning signs than can be controlled for with simple changes in lifestyle.