If the unit has sufficient billeting space they may require you to have a room so the military does not have to pay BAH for a young Soldier living off post.
If, on the other hand, billet facilities are filled up they can authorize you to move off base. Usually they offer this to more senior Soldiers first.
Bottom-line: most commands can make the Soldier maintain a room in the billets, and they can usually live off post as long as they maintain their room to standard, make all formations, and are not late. If they do not maintain their room and they become a problem child, the commander can simply revoke off post pass privileges and then the Soldier must remain in his room.