다가 잠들다

fell asleep in the middle

-다가 marks an activity that got cut off, and 잠들다 is dropping off, so the whole thing is falling asleep part-way through doing something: 공연 보다가 잠들었나 봐요 'he must have nodded off during the show', 기타 치다가 잠들었습니다 'fell asleep playing guitar'. Its close neighbour 고 잠들다 puts the sleep after a finished action instead of interrupting it.

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