What makes a speaker perform well at low volume?

A good amplifier is the biggest contributor, being able to manage the musical spectrum faithfully at low volume is not trivial.

My experience indicates that more efficient efficient speakers usually "perform well" i.e, deliver music and detail at lower volumes.

I agree that this is not a trivial issue, and certainly not a newbie one either.

I am in the camp the music sounds best within a narrow range of volume. This is most often very close or a few dbs louder than the recorded volume. I find that music that is excessively loud tends to become unrealistic. Whether this is due to room acoustics, speakers, amps, etc is open to debate (but please don't). It's probably a combination of all those factors. I suspect the room acoustics is likely a huge factor.

When music is too low, the instruments lack weight and palpability. The best example I can give is trying to convey the image of massed strings, like a violin section in a full orchestra. This is extremely difficult for a stereo to do, and I believe a speaker needs to move a critical amount of air to achieve this effect. At low volumes, it just doesn't sound like a full string section. I now have my stereo tweaked so that it does convey that elusive massed string effect, but it needs to be at least at a concert-going volume. My stereo can convey alot of detail at low volumes, but a good volume is important for having a connectedness with the performance.

I suspect that all this comes down to listening preferences, music preferences, stereo preferences, room acoustics, and the components as well. Good luck in your quest...I suspect you'll need it.

This is very important to classical music, as it is not usually very loud live. Next time you're at an orchestral performance, notice that you can easily hear someone's sniffling nose 5 seats away, or your own feet shuffling, on all but the loudest of crescendos. Most stereos have to be turned up much louder than the live orchestra to convey the same richness and excitement. If you can get involved with the music at low volume, you have a very special system indeed.
Excellent question, I wish I had the answer.