Triac circuit resistor tied to motor
My guess is that it's designed for a fan speed control with a minimum speed.  When the triac is off, the circuit is completed by the resistor, the motor sees reduced current, and turns at lower speed (with lots of slip).  When the triac is on, the motor goes fast.

Presumably the PSC motor is designed for this sort of service -- I suspect that some randomly-chosen induction motor would likely overheat.