From what I understand:

If a prisoner was termed as ‘exchanged’, it does not necessarily mean that he was traded for another soldier from the opposite side and went back to fighting. Due to the logistics of actually transporting a prisoner to some common trading place (such as City Point) and that Grant did not want to trade soldiers, a policy was set up, the Dix-Hill Cartel.

A soldier that was captured might be placed in a local prison camp and then put on a list of ‘paroled to be exchanged’. This would mean that the soldier would pledge not to take up arms against his enemy. He would then be delivered to his own side under this agreement. The prisoner would then stay in this ‘purgatory’ camp (an exchange battalion) overseen by his own side where he would be with other prisoners of the same status until officially exchanged. When the soldier was officially declared exchanged, he could return to his fighting unit.

The actual process is a little more complicated, but I think you get the gist. I really do not know the specifics, but a little research might provide more details. R. Hugh Simmons, the editor of ‘The Fort Delaware Notes’ provided me this information.

I could have misunderstood the information, so let me know if something different is discovered.