Coated woofer - why?

Coating a speaker will reduce the amplitude of cone break-up and the associated resonant behavior. Especially in the upper frequencies of the drivers range.

Those KEF drivers were coated with a doping compound called plastiflex, which did exactly that.

Smooth response and low coloration are the audible results.

Let me add, since coating the woofers was done by KEF as part of their construction, I am not sure you could call this a "mod".

An old (20+ years) speaker with multiple previous owners has a coated woofer - why would this mod be made? What are the implications for SQ? Speaker is a LS35A type with original KEF B110 woofer.

Let me add, that if you are in need of direct replacements, the company Falcon Acoustics, sells all replacement parts.

https://www.falconacoustics.co.uk/bbc-ls3-5a/falcon-ls3-5a-b110-drive-units.html  

It couldn’t hurt to think about replacing those old woofers. Surrounds, glue, etc tends to age.