If it's a 12db per octave slope on the woofer, then only a coil is in series with the woofer's voice coil. The cap would be across the coils.
I've have seen voice coils so warped that it took lots of power to make them move. Of course none of us know what the real problem is here, but we can play the odds. I worked on a Dynaco A25 in which the woofer's voice coil was actually on fire at some point, as the entire assembly looked like a fire scene.
Just sayin'.
Also, if the speaker is blown, there are many resources available to re-cone it, so it's not like its the end of the world......
Wayner