-다가 indicates an action was interrupted or changed - "while doing X, then Y happened."
I fell asleep while watching TV.
Often implies the first action was interrupted by the second.
Interruption or switch
- 가다가 멈췄어요 (was going then stopped)
-다가 vs -면서
- 다가 = interrupted/switched
- 면서 = simultaneous throughout
Same subject usually
- Both actions by same person
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