I think you may have a partially blown woofer.
When you buy something used, it is not too uncommon that the units are being sold because there is an issue.
In many cases a speaker driver fails completely because the voice coil winding wire is physically broken due to too much heat. Or the little tinsle wires between the terminal and the moving diaphragm breaks for the same reason. Sort of like a fuse blowing. In that case the voice coil tests as an open circuit electrially and the unit is dead.
In your case it is proably a warped former - melted glue - partially displaced voice coil winding. The former is the cardboard-like cylinder on which the voice coil wire is wound. There is also some glue holding the windings in place.
There can be long term high levels of drive which heat up the voice coil, like a toaster. Then the glue melts and the windings come out of place.
The mechanical issue is that the voice coil on the former is sitting in a relatively narrow ring-shaped gap. With deformation due to heating, the voice coil bloats or deforms and binds in the gap.
The result is that the speaker driver works to some extent at high freqs but the bass is gone. A normal diaphragm assembly will move smoothly when you push gently with an open hand and indeed resonate. A warped and binding voice coil feels jammed or gritty.
My guess is that you will find this when you take the woofer out of its housing.
BTW I took apart a pair of failed woofers owned by a young relative. They were totally dead so I took an X-acto knife to the diaphragm - voice coil units. The windings were out of place, glue was melted and there was charing.
In many cases of second hand purchases, it is the tweeter which has been damaged. That was not the case with those. I can only guess that someone drove them with the bass control all the way up and the loudness switch "on".
Wm McD