Edgar Derby is the unfortunate high school teacher and slightly older-than-average soldier who winds up getting shot at the end of the war for stealing a teapot from the rubble of Dresden. He is tried and executed by a German firing squad, and Billy is among the group of POWs who have to dig his grave.
The narrator comments on the dramatic irony of the situation: Edgar survives the misery of the firebombing of Dresden only to be executed for a trivial "crime" (1.3.19).
During the war, though, Derby is one of the most idealistic characters of the bunch: he winds up being elected head of the American group of POWs, and he also tells off creepy American Nazi Howard W. Campbell, Jr. Derby dreams of the letters he would write to his wife if he could, telling her that he is safe. He seems like a nice guy, but that's not enough to save his life.