1) simple case - two wave pulses canceling on a string. The potential energy that "vanishes" as the string goes flat is stored in the increased Kinetic Energy of the string moving through flat.
2) For every region of destructive interference, there are regions of constructive interference that maintain the energy balance. I imagine that somewhere just outside noise canceling headphones, there is a region of increased sound.
What your ears feel is the pressure variations - if the displacement is not there, there is nothing for your ears to feel - either as sound or as damage.