Does noise-cancelling cancel out the impact of a loud noise on your hearing?

So what I am trying to ask here is whether noise-cancelling headphones are actually working because the listener hears both, the noise-cancellation acoustic wave as well as the original acoustic wave, at once which synaptically cancels out to silence or because the ossicles don’t transmit any vibration if both acoustic waves would move the bones in contradicting directions?

Let’s assume there is a listener with hypothetical noise-cancelling headphones that cancel out any acoustic wave of any amplitude and a nearby source of acoustic waves with very high amplitude. Which of the following effects is closest to what will actually happen:

• The listener’s hair cells in the inner ear are damaged and both acoustic waves are transmitted by the ossicles
• The listener’s ossicles are damaged because the energy of the contradicting air vibration of the acoustic waves discharges onto the ossicles
• The listener’s hearing is unaffected and nothing is damaged because there is no air vibration when acoustic waves of opposite amplitudes pass through the same space
• (The acoustic waves cancel each other out before they even arrive at the ear canal)

Please excuse me if I have used incorrect terminology, I am not an expert in either of the topics. Additionally, I am unsure if this is the right stack exchange site to post this question on but since it’s mostly about acoustic waves I thought it would fit best here.