The potential energy of an electron becomes more negative as it moves toward the attractive field of the nucleus; in fact, it approaches negative infinity. But because the total energy remains constant (a hydrogen atom, sitting peacefully by itself, will neither lose nor acquire energy), the loss in potential energy is compensated for by an increase in the electron's kinetic energy (sometimes referred to in this context as "confinement" energy) which determines its momentum and its effective velocity
Though it is quite logical that an electron may fall into the nucleus, however according to quantum mechanics an electron has wave-particle duality i.e. exists as wave and particle both. Hence it cannot go in to the nucleus as it violates laws of quantum mechanics.