I always thought of it as a shroud, or something they wrap him in before they stuff him in a coffin. Sort of like a cotton bag you wrap around a deer or elk carcass to keep the flies out. I think the idea that he dies after the song is just a matter of poetic license.

Mothers don't let your babies grow up to be turtle boys. I've got to make it to Rose's back door. But I'll be better, Doc, as soon as I am able.