Grammar
-다가
Meaning
Intermediatedaga
Says one action was under way when another cut across it. The interruption is the point: 시위를 이끌다가 총격으로 순국했다 means they were leading the demonstration and were killed in the middle of doing so. Swapping it for -고 ('and then') would make the two events merely consecutive and lose the sense that the first was stopped.
Form
Attaches to a verb stem: stem + -다가, often shortened to -다 in speech. The subject of both clauses is normally the same. Add the past marker (-았/었다가) and the meaning shifts: the first action finished completely before the second, and the second often undoes it — 갔다가 왔다, went and came back.
Examples
길을 걷다가 친구를 만났습니다.
I was walking down the street when I ran into a friend.
값이 오르다가 지난달부터 떨어졌습니다.
Prices had been rising, and then fell from last month.
열전 특성을 분석하다가 이 신호를 발견했습니다.
They came upon this signal while analysing thermoelectric properties.
Common mistakes & nuance
The interruption is the whole point, and that is what separates it from -고. 밥을 먹고 나갔다 means they ate and then left; 밥을 먹다가 나갔다 means they left in the middle of the meal. Learners who reach for -다가 as a general 'and then' will keep implying that things were left unfinished.