Noise cancellation

I know there are programs, like Audacity, that will null out background noise.  You give them a sample of just the noise and they subract that from the whole audio track. Does anyone know what these programs do if the noise sample is louder than whats in the audio track? Suppose, for example, you shot a video walking around a store while the manager talks about the various items.  The noise you want to null out is a generator at a building site across the street.   But this noise will be louder when we're walking near the front of the store than when we're at the back.  If the noise sample being used to null out the noise is louder than  the noise in the audio,  will noise get added back in, or will it the track noise just go to zero and stop?

Thanks