고 남다

what's left after doing that

The -고 clause is what used the rest up, and 남다 names what survives: 다 먹고 남은 마지막 2조각 "the last two pieces left after everyone ate", 쓰고 남은 깜빠뉴 "the pain de campagne left over", 건져내고 남은 물 "the water left once you scoop the solids out". Most of these lines are food, which is where the phrase lives. One uses it of a person instead: 안 가고 남아있던 사람, the one who stayed behind.