What happens when one of the three lines supplying a three-phase induction motor becomes open-circuited?

The motor, if already running, will continue to run as a single-phase motor on the remaining single-phase supply. The condition is called single-phasing. If the motor is loaded to more than about 30 per cent of full load, the currents in the motor windings tend to become excessive and overheating occurs.

With one line broken, the motor will not start up and, due to the heavy standstill current, burn-out is likely unless the motor is quickly disconnected.