What happened after a battle ended in the civil war?

If the losing army did not manage to escape, they would be ordered to hand in their weapons ("Stack Arms!"), and then be transported to prison-camps, from where they might be exchanged for prisoners on the other side.

When Grant became General-in-Chief in March 1864, he stopped prisoner-exchange, knowing that the manpower balance would then be tilted against the Confederates, thus shortening the war.

It did - but at a terrible cost. For the prison camps became horrendously overcrowded, at a time when food supplies were running out for the armies and civilians alike. Naturally prisoners came last in line.