What damages a card is too much heat, which wears the components out. Cards have automatic temperature limits at where the cards underclock to prevent damage.
The other thing that can damage cards is too much voltage. While more voltage leads to more heat, voltage itself can be too much for the components to handle, literally frying them.

So underclocking puts less stress on components, and actually increases their lifespan. And as have been said, the thing that can happen is that the drivers malfunction, and have to be reset.