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.