-고 attaches whatever came just before and 잠들다 is dropping off: 책갈피를 끼워두고 잠들었어 'put the bookmark in and fell asleep', 햄버거 먹고 잠들 때가 저는 진짜 행복하거든요. Its near neighbour 다가 잠들다 is different in a way worth keeping straight: -고 puts the sleep after something finished, while -다가 has the sleep interrupt an activity halfway.