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Cheap audio cards and some expensive ones use volume control in the digital domain. This is done by slicing bits, e.t. left shifting the values. Using 8 bits as an example you might have a stream of "numbers" like this:
11010110
11001111
11010101
....
In order to reduce the "digital" volume, all that is required is that the numbers that are sent are all reduced by a fixed ratio, e.g.:
00001101
00001100
00001101
....
As you can see, you lose information as the digits disappear. Left shifting by one bit halves the electric meaning but is perceived as ~ 0.7x decrease. To perceive half the volume, the digits must be shifted by 2 bits, quarter - 4 bits. So if your DAC is working in 16-bit mode you are listening with 12-bit precision at 1/4th of max volume.
There are high end solutions with digital potentiometers at the analog side.
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