The grammar form is [base verb] + -다가 (가 can be omitted), meaning "while / on account of doing something, another unwanted thing happened. It is similar to giving a reason for a bad occurrence, when the reason is another action one was engaged in. 있다가 is just one example: 있다 + -다가 -> 있다가 = staying / being somewhere (있다 as an action verb means to stay or spend time somewhere). Examples: - 아침에 늦게까지 자다(가) 회사에 늦었다 = Oversleeping myself / Because I overslept myself, I was late for work. - 졸다가 내릴 곳을 지나쳐버렸다 = As I was dozing, I passed my stop.

What is the context? TTMIK Level 5 Lesson 9 may help you :)