What happens when the supply of energy-rich molecules in a muscle is used up?

If there is no energy left for the muscle, then the muscle is tired and needs to rest. This is because there will be no more energy (in the form of ATP) to supply the excitation-contraction coupling mechanism (the mechanism for muscle contraction, which needs energy).

In the event of this situation, the person will not be able to move the muscle with depleted energy source at all.