I would seriously not be surprised to find that fat people have starved to death without their fat cells releasing fat, and blinded by preconceptions, nobody managed to notice or note down when this occurred.

This happens all the time. We give it a different name depending which cell type starts dying first. Usually it's heart muscle, in which case we call it heart disease, but sometimes it's nerve cells (alzheimers) or the immune system (cancer). General death of a cell type can have many different causes, so it's easy to avoid acknowledging this one in particular.