In the case of Pemberton's Vicksburg garrison which surrendered July 4, 1863, paroled prisoners remained with their units, marched homeward under command of their officers and were to ultimately wind up in an Exchange camp until exchanged.
While enroute home, Pemberton got Pres. Davis to allow the men 30/60 day furloughs to return home, but meet at a given date at the designated exchange camp.
George Martin