[Arran]

 I think that the dampening material is a strip of rubber across the back of the passive radiator that suspends the center of the cone, at least on the 9'' sized ones. The cones in those remind me of the cones used in a balanced armature type permanent magnet speaker so the design was probably based in part on one of those. 
 Unfortunately it looks like the rubber perishes sometimes, on one of the ones Ron was selling it had actually melted, but even if it had not done that I'm sure that the condition of the rubber would have deteriorated enough that it would not perform as well as it did when new. It would be an interesting project to rebuild a set of those passive radiators, though I haven't run across a 3116X, 37-3116, or a 38-3116 for sale in my area yet.
Regards
Arran