Something similar to social service but focusing on compassion and care as you described. Inmates that committed small crimes would have the opportunity to reduce their jail time by helping others.
People who have committed crimes very often did not grow up receiving compassion and care, and therefore are those who need it the most.
By having these people doing compassion work you make them better humans and they will be less likely to commit crimes again. They would feel that they offer something in society and others need them. It is a lesson you don't easily learn in jail.
Based on the psychometric and criminal profile of the inmate, they would match to an appropriate place. You wouldn't appoint a drug addict to a facility where they would have access to drugs, like a recovery facility or a homeless center. Also, not every person would be eligible in the first place. Dangerous murderers for example would not be suitable for such a service. But people having committed smaller crimes, yes.