We have some of that already--conservative re-education--but I do like the idea of an expanded system.
Every month, depending on various skills, they might have a chance of doing something interesting--perhaps even recruiting sleeper prison guards, if they're persuasive or seductive yet.
How about this:
High Writing skill: May write a memoir from prison, changing public opinion of the LCS.
Low Heart: May get into a fight, sustaining injuries, being killed, or killing another prisoner (extending their sentence).
High Religion, high Wisdom: May "get religion" in prison, leaving the LCS and possibly adding Racketeering charges to their superior.
High Intelligence: May take a random college class while in prison, for free.
High Persuasion or Seduction: May recruit/seduce sleeper prison guards.
High Agility, Disguise, Stealth: A chance each month of escaping prison independently.
High Law: May be able to get death sentence commuted to life imprisonment, or shorten existing sentence.