If it helps, I would use "prison system" to refer to the general group or system of prisons that people are locked away in. Example: "Citizens were concerned when the state government cut funding to the prison system." If you want to refer to the time someone spent locked in a prison, I would say something like: "The man served 10 years in prison before being released."

Do you have the complete sentence for context? As far as I know, it's not a set phrase.