Fuel pumps are designed to stop if a phase is lost.
This is due to the way the motor is wound (a star rather than pi motor winding).
The fuel pump will stop rotating and the windings will heat until non resettable thermal switches in the windings cut the power to the windings.
This is a safety feature to stop the pump running at low rpm and eventually overheating.
Many of the high powered motors (e.g. recirc fans) operate in a similar way.