Can Woofers Be Repaired?

I have a pair of rather generic (but for me, still adequate) speakers from the '80s, where the woofer on one speaker has deteriorated. Specifically, the rubber/foamlike substance that encircles the diaphragm and connects it to the outer rim that is fastened to the speaker body has deteriorated. The woofer sound is distorted because of this, but would function normally otherwise.

I posed this question to this forum around four weeks ago, and received a few responses as to what to do, but unfortunately, I found that the thread was since deleted, and I didn't copy the info I received then. Any responses (which I will be sure to promptly save this time), would be appreciated. Thank you.