The action of the motor has been fairly well described, but the system also has an effect on the action of the motor.
The motor will run with one phase missing but the back EMF will still be generated on all three phases. This is how rotary phase convertors work. If one phase has low voltage, the induction generator action will try to bring the voltage up on that phase and overheat while trying. If the phase is missing there is no load and no current to over heat the motor.
Now consider a plant where one main fuse has failed. The motor will continue to run on single phase and the induction generator effect will try to supply the load with the missing phase back to the failed fuse. A lot of large motors with no load may simply keep the voltage up on the bad phase without overheating. Think sawmill with the large motors left running during a coffee break.
This situation will not arise often, but illustrates the importance of looking at the whole system rather than just the motor. If the phase is lost in the motor controller the action of the motor may not be the same as if a main fuse or a distribution panel fuse has failed. If the phase is lost in the controller and the motor is under a light load there may not be any problems until the next time that the motor tries to start. Even if the controls are on the failed phase, induction generator action may keep the controls energized.
Bill
--------------------
"Why not the best?"
Jimmy Carter