Two Majorana states coupled to each other across a Josephson junction may host an even or odd number of electrons. Classical or quantum dynamics of the Josephson phase violates the electron number parity. Classical driving changes parity by ionization. Quantum fluctuations of phase (induced by charging energy) hybridize the odd and even sectors. We find the ionization rate in the former case and the hybridization amplitude in the latter one. These two effects share a connection to the quantum-mechanical problem of ionization of a discrete level, which is approaching a spectral continuum.