I never heard of a song for this story, but I believe "O'Henry" wrote the story or one very similar to it. There was a film made about 3 short stories by "O'Henry". One was about a girl with long hair who sold her hair to buy her husband a watch fob for Christmas, at the same time the husband sold the watch to buy her someting for her hair, I can't rememebr the 2nd story but the 3rd one was about someone in bed, very very ill who promised she would not die until the last leaf fell from the tree, Her husband glued a leaf on to a branch for her to see, this act kept her alive. I can't remember how it ends but I'm sure someone else will have seen this movie.