We show that, when an atom prepared in a high Rydberg state is one-photon ionized by a laser, a near resonance with some lower-lying state permits the formation of a nondecaying dark state of the coupled laser-atom system. This dark state traps population in an amount that increases to some upper limit as the laser radiation used becomes stronger. Thus the dark state formed causes a decrease in the Rydberg-atom ionization with increasing laser intensity, i.e., stabilization, which survives even for long times. This long-time stabilization is described by a simple zero-pole formula, and the physical meaning of the term long time is explained. We estimate, for model situations, the laser frequencies that ensure dark-state formation and maximum ionization suppression. The laser pulse intensity and duration that are required for the observation of the dark state are evaluated.