This paper discusses problems related to partial observation supervisory controllers with possibly faulty sensors in the framework of discrete-event systems. At initialization all controller sensors are operational such that all sensors correctly communicate their event observations to the controller. Sensor failures are unobservable. After a sensor fails, it sends no signals to the controller. Depending on the sensor failure dynamics, the controlled system could exhibit a bounded range of behaviors. We define languages that respectively define the minimal and maximal sets of behaviors that could be exhibited by a controlled system with faulty sensors. We introduce bounded discrete-event supervisory control problems for faulty-sensor control systems. We use a construction to test for the existence of controllers with faulty sensors for two different control scenarios. We discuss how to synthesize these controllers using standard supervisory control methods.