A/V + 은/ㄴ 채(로) is used when you start doing something (B) while maintaining a previously mentioned state (A). It differs from (으)면서, where the two actions happen and continue simultaneously. The clause attached to ㄴ 채(로) is always in a passive-but-completed state.
It roughly reads as “while in the state of A, I did B”, where A is not a necessary condition for B. Note that 가다 and 오다 are never used with this form.
이전 직장에서 몇몇 한국 선생님이 취한 채로 학교에 왔어요.
In my previous job some Korean teachers to came into work drunk.
여름 동안 그는 옷을 입지 않은 채로 집 안을 걸어다녔어요.
In the summer he walked around the house without any clothes on.
너무 더워서 옷을 입은 채로 월성계곡에 뛰어들었어요.
It was so hot at Wolseung Valley that we jumped in the river with our clothes on.
왜 문을 열어 놓은 채로 변기를 사용해요?!
Why are you using the toilet with the door open?!
셔츠가 차 문에 끼어있는 채로 출근했어요.
I drove to work with my shirt stuck in the door.
불을 켜놓은 채로 잠이 들었어요.
I fell asleep with the lights on.
신발을 신은 채로 모스크에 들어가면 안 돼요.
You can’t enter a mosque with your shoes on.