In my experience convicts want to work, in fact in most major institutions there are fewer jobs available than convicts wishing to do them.
I used to more or less make-up jobs for them, I had one guy (an amputee) who's only job was keeping the microwaves and water fountains in the cell-house clean.
That was not always the case, with the old field units they worked on road gangs and were employed by the Virginia DOT. That's gone now as DOT figured out it was more cost effective to hire contractors to do the work that the convicts once did.
Back then we raised our own livestock and had a extensive garden. The field units in a region would supplement each other with what we raised and grew. One camp might raise hogs, another cows, and another chickens. One provided us salt fish when the big herring runs were on.
All convicts worked either on the road (our primary mission), farm, or in duties on the unit like kitchen, sanitation, laundry, water treatment plant, general maintenance, etc.