How can you say a restaurant is closed down?
Like if a restaurant is closed down permanently. Completely out of business. 어떻게 말해요?

Question

Answer

'폐업했다' is using regularly.
For example, 내가 자주 가던 식당이 어제 폐업했어
But we use more this expression, 문닸았다 
For example, 내가 자주 가던 식당이 어제부터 문닸았데

Answer

Just a few days ago, in a drama, the main character said, "문 닫았어?" when a shop was closed.

Literally, it means, "The door is closed."

Also, he was talking to himself, so he wasn't using polite Korean like, "문 닫았어요?"

Further, in my experience, you do not use the same expression for, "What time do you close?" That would be, "언제 끝나요?"

That's what I was taught to ask by a store owner.

Answer

OOO(the name of retarant) 없어졌다.  -> this expression is the most common use. 
it's not limited in 식당. if any other store is disapear then you can say that.
문닫았다 is also used common. or 아예 문닫았나봐. 아예 문닫았어.

to a friend, 
영희야, 우리 학교 앞에 있던 식당 말야. 그거 결국 없어졌더라. 웬일이야. 손님도 없더니 망했나봐.  아예 문 닫은 거 같더라고.

in office,
김대리님,  저희 지난 번에 갔던 식당이 폐업한 거 같던데요. 오늘 회식은 어디에서 하실 거에요?