A permanent magnet machine with a hybrid cage and methods for operating same are disclosed. According to one aspect, the subject matter described herein includes a rotor and hybrid cage for an electrical machine, the rotor comprising a rotor body having a central axis and including a plurality of permanent magnets positioned to create a plurality of rotor magnetic poles distributed around a peripheral surface of the rotor. The rotor also includes a hybrid cage that includes conductive loops around each of the rotor magnetic poles, where the conductive loops are controllable to form a closed circuit or an open circuit around each of the rotor magnetic poles. A closed circuit may be created when a magnetic field having a field strength or change of field strength that exceeds a threshold magnitude is present, such as during a fault condition, and an open circuit may be created when a magnetic field having a field strength or change of field strength that exceeds a threshold magnitude is not present, such as during normal operation.