I think that the reason why Fye sleeps this way,his head covered by the pillow,is that he doesn't want anybody to see his face when he have nightmare, or when at night he feels a little depressed and let his smile disappear.
he certainly tries to hide his pain by concealing his beautiful face behind his hair!
after all,it is impossible for someone to smile 24 hour on 24,i'm not sure but peharps that Fye cries silently at night,and nobody can see his eyes!
well,it's just a supposition,but in other chapter,when Fye in about to break because of Kurogane,we always see his face covered by his hair,which give him a sad expression.