Why does starvation kill fat people?

No.13033787 ViewReplyOriginalReport
If you stop eating food, your body consumes fat instead (and eventually muscles, organs, etc). It gets energy from the fat in order to keep functioning. So how come a fat person will die after not eating for a few weeks? Why can't their body just keep functioning by consuming all their fat until they have nothing left?
>inb4 you need vitamins
So why can't they just take vitamin supplements, and not eat anything else? How come they still starve to death?