Nut Jobs. :)
Thats British for "Whack Job"
They are called 'Psychiatric hospitals' now, and the criminals with mental illnesses are just kept in the psychiatric ward of prisons.
So, I think there are about the same kind of jobs in the psychiatric ward of prisons, as there are in regular psychiatric hospitals. Like, psychologists and stuff.
You are asking two different questions. If you are a criminal there are jobs within a prison for you. There are tasks for those within an asylum.
I suppose in an insane asylum, with the right props, you can be anything you want if your munchausen is strong enough.