1.Not literally as it is, this expression is used only when two friends (either existing gender), happens to kill another one accidentally and one or neither of them never tried (to solve this problem together) to sing the same song of regret yesterday.
2. To paraphrase, "Sing (or sung) Yesterday's Music sheet", is to settle a problem between two friends (usually a love situation." So when saying sing or sung, it is meant to settle.
*interrogation of deceased person's friend*
Police: It's not entirely your fault
Boy/girl: No! It is! I should've been the one to Sing Yesterday's Music Sheet with him/her!