My grandfather used to sing this to me. He sang a sort of postlude, too, to a different tune which I have now forgotten.
I don’t know why pig mortality was something my grandfather was singing to me about, or indeed whether two grown-ups dying of broken hearts is really appropriate material for a four-year-old, but I don’t remember it bothering me at all. Some of my happiest childhood memories are of singing with parents and grandparents, so I don’t tend to think of this song as either absurd or depressing.
There may well be a “proper” rhythm or structure to this that I’ve missed; my performance, other than the multi-tracked “mmm-hmmmm”, is as I remember it.