“Never use the software volume slider, it throws away bits.” The first half is arithmetic and true. The second half — that you can hear it — is almost always false, and this shows you why by putting the answer in decibels of actual sound rather than in bits.
Each bit is worth 6.02 dB of dynamic range, so attenuating by 20 dB costs you 3.32 bits. On a 24-bit path that leaves 20.7 bits, and a signal-to-noise ratio of about 126 dB. On a 16-bit path the same cut leaves 12.7 bits and 78 dB.
Bits alone are a useless way to think about this, because the question is never “how many bits”. It is where does the noise floor end up relative to your ears. At a 100 dB peak, that 24-bit path puts its noise at roughly −26 dB SPL — below the threshold of hearing, below the noise of any room you have ever been in. The same cut on 16-bit puts it at about +22 dB SPL, which is audible in a quiet room at night.
There is also a practical ceiling you hit long before the maths bites: a real DAC's analogue output stage manages 110 to 125 dB of signal-to-noise. Below that figure the digital arithmetic simply is not the limiting factor any more, no matter how tidy it looks on paper.
Modern software mixes in 32-bit float and only reduces to the DAC's word length at the very end, so the “lost bits” never exist as a step in the chain. Dither turns what would be quantisation distortion into a small amount of steady, benign noise — you lose signal-to-noise smoothly, you do not get audible stair-stepping. And bits are lost from the bottom of the range, not the top: nothing about the music changes, only how far down the silence goes.
The genuine failure mode is different from the one people worry about: a large digital cut combined with a lot of analogue gain. That amplifies the DAC's own analogue noise along with the music. If your amplifier has a gain switch, use it before you use the slider — and if the problem is hiss with sensitive in-ears, attenuation after the amplifier is the only thing that lowers the noise floor along with the signal.