Lose 1 MSB for every 6.02dB attenuation is the basic rule.
It's really not as bad as you might think.
In the following image, the top trace is full volume, the middle trace shows what it "looks" like with 60dB attenuation using the same visual scale (it looks like there is nothing left), the bottom trace zooms in on the -60dB (1/1000th) version to show what's left, which isvery close to what you started with.
-60dB takes your playback from "loud" to "almost inaudible".
The traces represent "voltage" that would be output by the DAC.