The thing about smoke & fire is... Eventually the "fuel" is consumed it should stop burning.
The odor may linger for a long time but it should stop
producing odor.
If the odor isn't too bad and it still works, maybe you can live with it.
...There is one possibility - I wonder if you have a DC offset out of your soundcard/interface, and I wonder if the sub's amp goes to DC?
Can you see the woofer? If so, does it pop-in or pop-out when you connect the input and does it stay offset from it's neutral position? Or, does that happen even before you connect your soundcard/interface? ...If you've ever connected a battery to a (passive) speaker, that's what I'm talking about... After the initial click/pop, the speaker sits there consuming energy (and heating-up) without making any sound, Till it clicks/pops again when you disconnect it. (If that happens with no input connection, there's a DC offset in the sub's amplifier and that's a defect.)
It's also possible for your
audio to have a DC offset (usually caused by recording with a cheap soundcard).
But... Most likely, the sub's amp would filter-out any DC and this is probably NOT the problem.. It's just one possible way to get heat from the voice coil without sound.
P.S.
Actually, it could be subsonic frequencies... It doesn't have to be DC (0Hz). So if you can see the woofer, also look for "excessive" woofer movement and maybe try a high-pass filter around 20 or 30Hz.