If energy is only found in discrete amounts what happens when the amount of energy falls below the minimum individual unit? does it have a floor or ceiling function or does it matter what type it is?
The answer is that it's impossible. If energy is quantized then the smallest you can have is some amount of energy $\epsilon$, and any measurement you make will give a result equal to $n\epsilon$ where $n$ is some integer. If we measured an energy less than the smallest quanta, then we would either redefine the smallest quanta, or we would reconsider our current understanding.