Answer:
It's from Shakespeare's Hamlet, in Ophelia's mad-speech. It means, literally, that someone (They) carried someone else (him) without any burial shroud (barefaced) to place him on to the platform or stand where mourners could come and pay their respects before they buried him. When she says it, in the midst of odd songs and little catch-phrases, it is a startlingly strange reference to death and funerals and such, which causes us to assume that "he" probably refers to her father, Polonius, who has just died and been buried. In fact, one of the next lines is: "They say he made a good end," which is a statement that people at the time often said of those who have "died well," that is, died in God's good grace or died bearing their pains graciously. On a deeper level, the statement probably indicates to us the origins of Ophelia's madness: having seen her father in such a state-- barefaced, easily seen without any burial shroud and also probably displaying openly the lethal wound given him by Hamlet--her rational mind could no longer bear the grief and the conflict between loyalty to him and loyalty to Hamlet, and she cracked, went insane. The fact that she says this statement suddenly, in the midst of mundane other little snippets of songs and oddities, probably means that her mind is trying to "move on," so to speak, but the horrible memory keeps breaking through. Today we might call this Post-Traumatic Stress Syndrome, having sudden "flashbacks" of what is haunting her, although perhaps Ophelia is a more on the psychotic side of it in a true psychosis of some sort.