This work considers the problem of control of nonlinear process systems subject to input constraints and actuator faults. Faults are considered that preclude the possibility of continued operating at the nominal equilibrium point and a framework (which we call the safe-parking framework) is developed to enable efficient resumption of nominal operation upon fault-recovery. First Lyapunov-based model predictive controllers, that allow for an explicit characterization of the stability region subject to constraints on the manipulated input, are designed. The stability region characterization is utilized in selecting `safe-park' points from the safe-park candidates (equilibrium points subject to failed actuators). Specifically, a candidate parking point is termed a safe-park point if 1) the process state at the time of failure resides in the stability region of the safe-park candidate (subject to depleted control action), and 2) the safe-park candidate resides within the stability regi...