Electrons can get localized in the nucleus, but it takes an interaction to make it happen. The process is known as "electron capture" and it is an important mode of radioactive decay. In electron capture, an atomic electron is absorbed by a proton in the nucleus, turning the proton into a neutron. The electron starts as a regular atomic electron, with its wavefunction spreading through the atom and overlapping with the nucleus. In time, the electron reacts with the proton via its overlapping portion, collapses to a point in the nucleus, and disappears as it becomes part of the new neutron. Because the atom now has one less proton, electron capture is a type of radioactive decay that turns one element into another element.