Talks of possibility of electrons to exist in any energy level has two discrete dimensions; first whether they can assume any given energy level. The answer is no. That is against the very stability of atoms (and hence of the entire universe). That would have led to breaking down of things in slightest of provocations. Think of the situation, you are switching on the lights of your room and all the furnishings are gone! That does not happen. So, the electrons can assume only certain permitted energy levels that satisfy Schrödinger's wave equation.
Another dimension is that whether electron in an atom can exist in any of the pemitted energy levels. Here, the answer is yes. The reason is, according to modern atomic theory, solutions to Schrödinger's equation describe discrete atomic energy levels and the probability of finding an electron therein. Since Schrödinger's equation is a theoretical statement, an infinite number of energy levels exist. However, when we place the electron for our known atoms into the energy level structure, the electrons from even the largest known atom all fit in just seven energy levels. There might be some theoretical discussion about the existence of eighth or higher energy level, though. An elecctron can occupy any of these energy levels depending upon its state of excitation (or, energy content). When the electron sitting in a lower energy level receives energy, it jumps up to a higher orbital, and as it loses energy, it falls back down to the lower energy orbitals and releases the additional energy.