V + 던 차에 shows that you intended to do something but then a second action occurred that meant the first action has no chance of happening. Unlike (으)려던 참에 and (으)려던 참이다, the emphasis is on a sense of a total U-turn in the situation:
약속 장소에서 30분 기다린 후에 나가던 차에 친구한테 전화가 와서 다시 약속장소로 갔어요.
After waiting for half an hour at the meeting place, I was about to leave, but then my friend called so I went back to the meeting place.
일을 끝내던 차에 상사가 업무를 더 주어서 야근을 하게 됐어요.
I was about to finish work when my boss gave me even more duties so I ended up doing a late shift.
취직이 잘 안 되던 차에 누가 추천을 해 주어서 면접을 보았어요.
I was having trouble finding a job when someone recommended me and I got an interview.
사표를 제출하려던 차에 부장님이 저를 승진시켜 주셨어요.
I was planning to hand in my resignation when my boss offered me a promotion.
일자리를 찾던 차에 마침 좋은 자리가 생겨서 다행이에요.
I was hoping to find a job when all of a sudden a good position came up, which was lucky!
음식을 만들려던 차에 친구에게서 전화가 와서 외식하게 됐어요.
I intended to make some food, but my friend called me and we ended up eating out.
바레인에 차로 가려던 차에 사우디 정부가 사우디와 바레인 사이에 대교를 폐쇄해서 여행이 취소됐어요.
I was planning to drive to Bahrain but the Saudi government closed the bridge between Saudi Arabia and Bahrain so I had to cancel.
어떻게 하면 좋을까 하고 생각 하던 차에 갑자기 해결책이 떠올랐어요.
I was thinking about what to do, and suddenly the solution came to me.
학교에 빚을 갚을 여유가 있을지 없을지 걱정하던 차에 복권을 샀다가 당첨되어서 쉽게 빛을 갚을 수 있었어요!
I was worried about whether I could afford to pay off my school debts, but I won the lottery and I could easily pay it back!