Removed my Audible Illusions Mod 3 from rack after 16 years and feet have turned to goo

Try Goo Gone.

I 2nd the Goo Gone product,doesn't have harsh chemistry and really works.
I believe all wal marts or similar stores sale it.

You may need some new footers though.

Kenny.

I had a similar thing happen with some rubber footings I had beneath a center channel speaker. It's a good reminder to everyone to move their equipment every once in a while so that it doesn't happen again.

How/where did you have it stored, e.g. humidity, temperature, etc.? Wonder what does it look inside...

My system was in my 14x25 medium room in my basement. So the temp is not hot or to cold . The transformer coil was on spikes . The main part of the preamp just sat on the rack. I think it all depends on the the product used by the manufacture . I have other 
pieces of equipment of same vintage and no problems with the feet.