I presume by loudness you mean an increase in the bass and treble to match the roll-off of human hearing as sound gets quieter?
Re the muso, others have pointed out the option it has.
I have often suggested that there is a case for that in full hifi systems but not with the crude on-off loudness button used on boomboxes and used to be found on cheaper hifi systems some years ago: Ideally there should be an option to switch in compensation that gradually changes the frequency response as the volume control is lowered, though it would need a means of calibrating in the room because it would vary hugely with power amp, speaker sensitivity listening distance and room (calibration would only be needed once at the start unless something is changed). I guess would be tricky to implement well, and it would take an innovative manufacturer to do it. However, potentially someone could do manually for themselves using DSP.