Can low voltage level damage home appliances?

The risk of loss is high.

To understand the explanation better you need to know the following:

Ohm's law: At constant temperature and resistance, the voltage is directly proportional to the current. That is, as the voltage falls, the current decreases.

• P = V * I: is equal to the current of the power voltage. Where V = rated voltage and I = current drawn by the instrument.
• Many practical loads use different combinations of resistors, capacitors, and inductors.
• Each device has its own voltage rating and current (or power rating). When a low voltage is applied to one device, the device will operate on other operating parameters (ie, current and power will change).
• When a low voltage is applied to an appliance, the device will draw more current to meet the rated power (P = V * I). That is, there will be more current through the conductor. The current carrying capacity of the conductor in the equipment will determine the cause of the damage.

When the current drawn by the conductor exceeds the current carrying capacity of the conductor, it generates more heat which can cause wire, insulation failure to burn and equipment will be damaged.

If the current passing through the conductor is capable of carrying it, the device will not suffer damage. - This explanation is for inductive loads like a motor.

For resistive loads, lower voltage means less power. When a low voltage is applied to an incandescent bulb. It will glow with low wattage (ie the bulb does not give the final brightness).