Help me understand how stored fat is used by the body?

People do die from the fats building up.

When you eat you partly use the energy, because we are always using calories, even when we just sit in a chair and do nothing, and then extra carbs get stored as glycogen and proteins is broken into amino acids and stored in muscle, and then once your stores are full everything else goes to fat. When you exercise the body pulls from storage, like running would pull a lot of glycogen storage, and if you completely deplete that is called “hitting the wall.” yu may have heard that expression before. Anyway, carbs are best for certain body needs, protein for other. If the body runs low it goes to fat and can convert the fat to work in place of the others, but it is not as as efficient. At any given time we are using carbs, fats and protein all at once, it depends on the demands we put on the body and what we are in short supply of.

It’s a complicated process and not conducive to a short summary.

Here’s a clear (but not overwhelming) five-page version of How Fat Cells Work,. both coming and going, and with pretty pictures.