In elementary QM, an electron is typically viewed as a cloud around a proton. The idea is that it's position can only be determined once a measurement is made. The probability that the electron will be found in a certain region is determined by it's wave function.
For background see the question Is it that electron of an atom can be found anywhere in the space?
Assume a hydrogen atom in the ground state.
Now, there is chance, however small, that the electron will be found very far away from the proton. So far away, that it cannot reasonably considered under the proton's influence.
In other quantum situations, a particle can tunnel though a potential barrier if the barrier is finite. This allows a particle to escape as in beta decay. This is not exactly that situation, but the further away electron is found, the less influence the proton field will have on it. Is there a point where the electron becomes unbound? And is it the measurement process that causes this to happen? Or if we observe enough non-interacting, isolated hydrogen atoms, will we observe that some of the protons no longer have a bound electron if we wait long enough?