Each of the 44.1 samples / sec is recorded using a 16 bits scale = some 65k different possible values. Lowering the volume to say 10% means recalculating this to a scale with less steps, so 6.5k max. This range must cover all passages from the soft to loud. So the DAC has less dynamic range to work with, and the poorer analogue signal goes to the amp that increases the volume again to the desired listening level, but especially the original soft parts will have suffered.
P.