Good morning.
Yes, it is possible.
Energy is a scalar quantity. The value of the potential energy is calculated the following way:
[tex]\mathsf{E_{p} = m\cdot g\cdot h}[/tex]
Where m is mass, g is the acceleration of gravity and h is the height.
Note that the height depends on the adopted referential, therefore, if we adopt, for example, a referential on the floor, if we dig a hole that has a depth of 1 meter, a ball that is put inside the hole will have negative potential energy due to the adopted referential, since h is negativa in this case.