How does low voltage burn out induction motor
In AC induction motors peak torque, that which is used to accelerate it from a stop or to recover from a step change in load, is related to the square of the voltage change. So if the voltage is 80% of normal, the peak torque capability of the motor will be only 64% of normal; at 70% voltage, you are down to less than half of the available peak torque. That means the motor is more easily able to stall and even if that doesn't happen, the slip of the motor will increase so if it pulls the same current, it will do less work, meaning the efficiency becomes poor and more of the energy consumed just becomes heat in the motor. Or if doing the same work, it will pull more current and current comes with heat. the latter scenario, more current, leads to hopefully tripping an overload protective device but the lower efficiency may increase the motor heating effects even though the current is low enough to not affect the protective device.

If the load on the motor has decreased as the voltage dropped, or the motor was originally grossly over sized, that may not be a problem. But generally a motor is selected to provide just enough power as was necessary.