When we say 'A -ㄴ/은 채(로) B', it means 'B happens while A takes place'. Consider examples below.
(1) '나는 눈을 감은 채로 노래를 듣고 있었다.'
In (1), the event A is 'My eyes were closed.' and the event B is 'I was listening to music.'. So (1) is translated as 'I was listening to music with my eyes closed.'
(2) '그 아이는 배가 고픈 채로 잠들었다.'
In (2), the event A is 'The child was hungry.' and the event B is 'He fell asleep.'. Thus, (2) is translated as 'The child fell asleep (while) hungry.'