This work considers the problem of handling the failure of purification equipment in a hydrogen production process. In this process, natural gas and superheated steam are fed to a heated chemical reactor termed a reformer to produce hydrogen. The effluent gas is further processed and finally purified in a pressure swing adsorber (PSA). The off-gas out of the PSA is used to provide heat to the reformer. The failure of the PSA results in the loss of the off-gas, precluding the possibility of the continuation of nominal operation. If not properly handled, this fault can lead to a shutdown of the entire plant. To achieve stable operation while meeting operating requirements, a model predictive control (MPC) based safe-parking framework is designed for the handling of the fault. The key idea is to drive the process to a feasible operating point that enables stable operation in the faulty mode. MPC is used to handle the multivariable nature of the process and operating constraints. It also guides the process to a different operating region while meeting operating requirements. The effectiveness of the safe-parking design is demonstrated through simulations using a first-principles model of the hydrogen production unit.