Most standards require that electrical equipment be tested at both nominal and hi/lo line inputs (around 10% deviation). I'm not aware of any standard that tests at a 20% line drop. There is no requirement to "protect itself", but there are various tests to ensure the equipment does not catch fire.

There are however, requirements for the utilities to provide min/max levels of line voltage and I believe a 20% drop in the supply falls below that minimum.

We performed UL testing on all our low voltage(<48V) products. Requirements were NORMAL operation from 85% to 110% of rated voltage and no permanent damage for voltages below 85% rated. Sorry, but I can't access UL spec docs to verify if these are the same limits for line (AC) appliances.

It has been 20 years since I qualified equipment with UL and CSA, but I recall testing 110 VAC rating continuously at 85VAC and 130VAC (about +/- 20%). Their requirements could have changed over the years, but because they are more safety oriented than performance oriented, the equipment could fail, but not in a way which was unsafe (fire, live access, etc.). If you need more information, I suggest you check with the current standards that apply to your specific product.