Absolute zero is considered to be the point at which all motion ceases. If this is the case how do you explain the theory that says that energy cannot be destroyed.
Because absolute zero cannot be attained. If we could "freeze" a sample to absolute zero, we could determine both the location and velocity of any particles in the sample, which contradicts the uncertainty principle. (It is impossible to know both the exact location and velocity of a particle -- the more certain we are about a location, the less certain we are of its velocity and vice versa)
Absolute zero is an unobtainable limit( limit in the mathematical sense). Thus we cannot lose or destroy the inherent energy in the system.
The First Law of Thermodynamics, or more commonly known as the Law of Conservation of Energy states that it is not possible to create nor destroy energy. Energy can only be changed between the six standard forms of energy: mechanical, electrical, radiant, thermal, chemical, and nuclear.
When we say that we are lowering the temperature of an item to absolute zero, what we are saying is that we are reducing the amount of thermal energy that an object has. We are not destroying the energy, we are simply changing the energy content of the object. The thermal energy is either being transferred out of the object into something else, or the thermal energy is being converted to two or more of the other forms of energy.
Absolute zero may mean "no motion" in a general sense as kinetic energy is linked to thermal energy (through the kinetic-molecular theory), but it does not mean the object has "no energy".