What is supposed to be on the surrounds is butyl. It is applied at the factory in liquid form (toluene is the carrier). It needs to be rejuvenated every 20 to 40 years.

The butyl seals the pores in the cloth surrounds to maintain the acoustic suspension properties of the speaker. A properly sealed surround is necessary for good bass.
Unfortunately, before RoyC performed testing on what to use to rejuvenate the surrounds, people used a wide variety of things to seal the surrounds. People used Permatex, latex, white glue, and other material. If that material cannot be removed and replaced with the proper butyl, then the drivers will not perform as they should. See this thread:
https://audiokarma.org/forums/index.php?threads/virgin-cloth-surrounds.637112/page-2 RoyC found that the using anything other than butyl resulted in stiffening of the surround over time.
I imagine you could use toluene directly to see if the surrounds are doped with butyl. The toluene will soften whatever butyl is on the surrounds and the surround will become more pliable and sticky. Hopefully, the surrounds have not been touched and only need more butyl applied.
The proper doping material can be obtained directly from RoyC (an AK member) or from vintage-ar on the bay.