Electrostatic potential energy increases as work is performed to separate unlike charged particles. Eventually the distance will be great enough that the force between them will be tiny, and you can completely separate them.

The concept of binding energy, so useful for interpreting gravitational systems, is also crucial for interpreting systems consisting of oppositely charged particles interacting by electrostatic force. The work-energy required to separate two opposite charges represents the binding energy of the system.

This conceptual framework of binding energy is essential for understanding chemistry, although you always need to keep in mind the augmentations to the model provided by quantum mechanics.

Think of the ionization energy of an atom as the work required to pull an electron free of an atom against electric force. The first ionization energy is the binding energy between an atom and its highest energy ground state electron. How much work would it take to pull the electron completely away from the atom? This is the ionization energy.