Almost every crime has a civil counterpart for the victim to sue for a judgement, and certainly any private property or personal violence related crime does. Victims of crimes can sue the perpetrator on their own if they have the resources to do so. As a practical reality, suing a homeless person to get back damages is a waste of money since the defendant won't have any money to pay, but a declaratory judgement against stealing or a restraining order could be used to keep the defendant away in the future, or give a victim more recourse if the defendant attacks them or their property again because they are now violating a court order. Judges can incarcerate a person in contempt of court independent of the District Attorney, though this again relies on the willingness of the government to enforce its own laws.
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