When someone goes AWOL and is apprehended, they are returned to their unit of assignment. When they are declared a Deserter (usually after 30 days AWOL), they, in effect, become a fugitive. If apprehended by law enforcement or military authorities in a Deserter status, they are turned over to the nearest Military Confinement Facility.
My knowledge is from personal experience with some that had been AWOL for a good length of time and were called deserters by the folks whose job it was to hunt them down.
At the time,I couldn't understand why the Military didn't jump at the opportunity to make examples of them.....except for the reasons explained.