Fat cell life cycle

I’m wondering about the life cycle of ‘fat’ cells. Since I’m totally ignorant on this topic, I have no idea of my question makes sense at all.

Somewhere I’ve picked up that when you start to look like me, your fat cells both grow in size and in number.
But what happens when you shed that fat? Do these extra fat cells continue to have purpose?
Cells live and die, so why would the extra fat cells keep dividing when there’s not alot of fat? Why would the body invest nutrients/energy in these?

Is there research into this?

Yep, there’s lots of research on this:

etc.