Evidence is presented of an unusual Rydberg system consisting of a helium nanodroplet containing a positively charged sodium ion and an orbiting electron. Rydberg states of this system with principal quantum number n<20 are found to be unstable on a nanosecond timescale. In contrast, Rydberg states with n≳100 are found to have a lifetime of 1.1 s. In addition, it is found that the ionization threshold of sodium doped helium is broadened and red-shifted with respect to that of the free atom. These observations are successfully reproduced using a pseudo-diatomic description of the system in which the interactions of the sodium and its ion with the helium are calculated as the sum of pair potentials.