Ordinary molecular dynamics surface simulations are particle-conserving. We have found that, while this restriction may be adequate for a majority of situations, there exists for most surfaces a range of temperatures where that is not the case. The critical temperature range is between preroughening and roughening. There, the surface equilibrium state is disordered and flat (DOF), implying a state of roughly half-filling for the outermost surface layer. A particle-conserving simulation, based initially on a well-defined, usually integer, number of crystalline layers, must phase-separate into two half-layered domains. We discuss evidence, indicating that this kind of phase separation is actually taking place in existing simulations.