Yes when your body is starving your body starts eating fat from your body.
However your body only eats your fat as a last resort after first exhausting the contents of your bodies digestive tract along with glycogen reserves stored in liver cells and after significant protein loss.
The body can also eat muscle and muscle tissue before it goes into fat eating mode.
But after all the other food sources for your body are depleted then body then goes into fat burning mode.
This is why the less food you eat the more weight you can lose.
However you still should never purposely starve yourself for a week or more to lose weight as that is unhealthy.
You need to eat at least some low calorie foods such as salads, apples, etc to keep your energy level up.
But the less you eat the more weight you'll lose because your body will eventually start burning that fat.