Answer: Yes it possible for a system to have negative potential energy, since the choice of the zero of potential energy is arbitrary.
Step-by-step explanation:
Potential energy is defined as the energy present in an object due to its position.
Mathematically, P.E = mgh
A potential energy can be negative also. This is because zero potential energy is arbitrary. For example, at the top of a building the choice of potential energy can be zero.
Therefore, the potential energy below the building will be negative.