Most single phase induction motors have a centrifugal switch which cuts-off either an auxiliary start winding or an auxiliary starting capacitor.
At lower RPM, the centrifugal switch will engage again, reconnecting the start winding and/or capacitor.
Neither are designed to operate continuously, and will eventually be damaged.
Now, even with a permanent split capacitor (PSC) motor, your torque curve will be abnormal if the speed range is large. The capacitor's reactance will vary with frequency, and the resulting field vector will deviate.