눈을 감기다 is incorrect, but 눈이 감기다 is correct 눈을 감다 is sound like he intend to close his eyes with his wll 눈이 감기다 is sound like his eyes is closed without his will for example, 저절로 눈을 감다 is incorrect. but 저절로 눈이 감기다 is correct 잠에 눈이 감겼다 is correct, but 잠에 눈을 감았다 sounds awkward to me. (I don't know it is grammatically correct, but it is awkward.) 잠을 자려고 눈을 감았다 is correct, and 잠을 자려고 눈이 감겼다 is incorrect.