Does ~다가 always require an action in the following clause? (Possibly found an exception)

Question

I am listening to Talk to Me in Korean's Iyagi #20 about dreams. I have multiple questions, but unless the mods recommend otherwise, I'll tackle them in separate question entries. So here is the specific dialogue that inspired the question:

[...] 집을 찾아다니다가 꼭 바다가 있는 그런 집이 나와요. [...] 그래서 제가 집을 찾아다니다가 결국에 똑같이 바다가 보이는 집이 딱 나타나요

So the predicate verb following 찾아디니다 is either 나오다 or 나타나다. These are both expressing the (for lack of a better term) inception of an object rather than a specific action by the subject. So I am confused since I thought that ~다가 has to be followed by an action done by the subject.

My second question is one I consider a larger question about the use of the object marker 를/을 versus the locative particle 에. For now though, I will simply ask:

Is the meaning described here 'Searched for the house' or just 'Searched the house'?

Answer 1

I agree with you. I find both sentences not so natural sounding. As you said, -다가 is used when the subject is the same in the subordinate and the main clause. Strictly speaking, the sentences are in grammar error (but of course, languages are always changing so we can't always be too strict). I think it is a shame that a language site uses such sloppy sentences in their examples (and I've seen other such cases at TTMIK).

Naver dictionary lists -다가's meaning in four categories (all related), and gives these examples for them, all of which have single subject in them.

1. 10년 동안 과장이었다가 부장이 된 사람. (부장 is a complement for the verb 되다)
2. 잠을 자다가 무서운 꿈을 꾸었다.
3. 못을 박다가 손을 다쳤다.
4. 날씨가 덥다가 춥다가 한다.

As for 집을 찾아다니다가, it means searching for a house. 집을 찾다 always means searching for a house to buy or rent, or just looking for certain house to visit someone. 다니다 in 찾아다니다 has the sense of moving around, so 집을 찾아다니다가 means "while searching around for a house".

Searching a house is expressed as 집을 뒤지다 (뒤지다 = search through, ransack, used more often for a drawer or room than house), or 집을 수색하다 (수색하다 is a formal term used by the police or military).