How could potential energy be negative?

Yes, potential energy can be negative. When you throw a stone up in air, it gains positive potential energy (m g h) considering ground as origin. Planets being in gravitational field of Sun, have negative potential energy. read more

The gravitational potential energy is taken to be zero as a matter of convenience - so that that zero potential energy is at an infinite distance from the centre of a spherical object. This is a choice, and other choices can be made. For example, the zero for potential energy can be chosen to be at the centre of a spherical object. read more

Typically, we’d use the ground as the zero point and measure the potential energy of an object suspended above the ground according to that distance. An object in a hole in the ground would therefore be said to have negative potential energy because you’d have to add energy to it to lift it out of the hole. read more