An important unresolved question in plasma physics concerns the effect of strong electron emission on plasma-surface interactions. Previous papers reported solutions with negative and positive floating potentials relative to the plasma edge. The two models give very different predictions for particle and energy balance. Here we show that the positive potential state is the only possible equilibrium in general. Even if a negative floating potential existed at t=0, the ionization collisions near the surface will force a transition to the positive floating potential state. This transition is demonstrated with a new simulation code.