Depending on the age of facility and security level, they do give inmates keys to their cells.

At the facility I worked at, the minimum-security and minimum-trustee annexes were configured such that inmates had a key to their cells. They couldn't lock or unlock the primary security lock, but they could secure their cell to a degree. Two locks, one only works with the key on the guard's set, and a handle lock that works with both the (cell-specific!) inmate key and guard key.