다가 돌아가다

head back after doing something

-다가 marks breaking off one activity to do another, and 돌아가다 is going back where you came from: 잘 쉬다가 돌아갑니다 "I rested well and now I'm heading back," 더 즐기다가 돌아갔답니다. Watch out for the trap: 돌아가시다 is the respectful word for dying, and it looks identical in these lines — 전쟁 중에 한국을 지키기 위해 싸우다가 돌아가신 분들 means those who died fighting, not those who went home. The honorific -시- and the context are what separate them.

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