When a person uses more energy than is taken in from their food what happens to their mass?

They lose weight. The entire point of a diet is to have a smaller energy input (food) than output (exercise). First you use up all the glucose in your blood, then carbohydrates in your body, then fat is broken down to make more glucose as fuel for your body.

If you keep going (starving yourself) your body uses up all the fat and breaks down muscles, which is not healthy for you!