If you connect the wiper to the output and you swap the other two pins, then the mis-behaviour you described makes sense.
A log pot has most of the attenuation on one side, while a linear one has it evenly spread across the range.
The perceived loudness of a sound corresponds to the amplitude of the produced sound along a logarithmic-ish curve. This is the reason why log pots are usually used for audio.
When talking about the perceived loudness of a sound passively attenuated with a pot, a linear pot would be similar to the effect you describe
the top 90% of the slider there is little attenuation.
but a bit less drastic. A log pot will respond nicely along the entire throw, UNLESS you wire it wrong.
The reason why you never hear it go to zero is also due to the mis-wiring: no pot will reach a reading of exactly zero, because when the wiper is at one end, there is usually a very short length of resistive material between the wiper and the pole which is connected to ground.
In the case of a linear pot, the ratio between the resistance R of that length of resistive material and the overall resistance of the pot is going to be very small, so that the gain will be $\frac{R}{R_{tot}} \approx 0$.
This is the case also for a log pot when you are close to one end (the one that should be connected to ground in your application).
At the other end of the log pot, instead, the resistance R of that small length of resistive material is going to be very large in comparison to the overall resistance of the pot, so that $\frac{R}{R_{tot}} \gg 0$.
