Switched systems play an imperative role in modeling many real industrial systems with abrupt changes. Due to possible exposure to unreliable and complex physical environments, switching dynamics may simultaneously face multiple faults, including the unexpected controller disconnect, the temporary mismatch between subsystems and desired corresponding controllers, and the intermittent disordering of mode transitions. These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution, thereby bringing significant yet challenging issues to be tackled. This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time (MDT). From a set-theory perspective, we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties. Moreover, the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof. A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.