Why does a person without carbohydrates still produce ATP through respiration?

If a person were to go on a non-carb diet (Atkins diet), they would feel a lack of energy since carbohydrates are a primary source of calories. However, the person's ATP supplies wouldn't be completely depleted and their mitochondria would still be actively involved in respiration. Please explain to me why. It's an AP Bio question that my teacher is requiring to answer WHICH HE NEVER FRIGGIN TAUGHT US.