If you stall the motor and let it draw as much current as it wants, the motor will be dissipating more energy as heat. What happens next depends on the design of the motor.
Some motors can dissipate all of the heat when stalled. Such motor can stay stalled indefinitely.
Some motors can't dissipate all of the heat generated when it's stalled. The heat builds up, the temperature of the motor raises. That can lead to a permanent failure of the motor (possibly a fire too). For this reason, some of the motors have built-in thermal protection in the form of a bimetal strip or a fusible link.