That's not the case. The 36th Mississippi Regiment was largely overwhelmed and captured at Blakely AL on April 9, 1865, and taken to prisoner-of-war camp on Ship Island during the next few days. Officers and men were sent to New Orleans on April 28, 1865, and thence up river to Vicksburg MS. They were released on exchange on the Big Black River on May 6, 1865.
Meanwhile General Richard Taylor agreed to surrender all troops in his department on May 4, 1865. The first paroles under this agreement were issued on May 9, 1865. Individual service files will contain paroles dated May 9, 1865, or later.
Someone who has a service file for a soldier from the 36th Mississippi Regiment captured at Blakely can reply with particulars about his parole.