How does the hardware volume control work?

I am just curious (and don't know much about HiFi): How exactly does the hardware volume control work? When I reduce the volume by 50%, is the least significant bit essentially dropped? Or can I still hear the lowest volumes, but the high volumes are lowered (I think this would be called "dynamic compression")?
As an example: Assume that I have a track that has a simple sinus wave, alternating between a very low volume (barely audible), and a very high volume. When I lower the volume, would the low-volume part of the track be lost entirely?
Would one method of volume control be preferable over the other?

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