How would the law deal with the Ship of Theseaus?

Say someone murdered 30 people long enough for every cell in the murderer's body to be different than they were when they committed the crime, and let's also assume they deeply regretted their crimes and genuinely felt sorry for doing them and never did anything bad again as to eliminate the possibility of them being imprisoned simply for being dangerous, why would they be considered the same person? What would make them the same person as the one that killed 30 people many decades ago? How could they be arrested if all the atoms that made up the person that killed all those people no longer exists?