The grips sound like celluloid-it was common in guitar parts from the 50's, and deteriorates when held in a place that collects and concentrates its off-gasses.
If you have grips that are beginning to flake or deteriorate, flooding the surface with C/A (cyanoacrylate, or 'super glue') has been effective in stabilizing the decay. Used well, it can also build up damaged areas and fill cracks and other faults.
Look up 'Dan Erlewine' and check out his tips on dealing with similar situations. (BTW, Dan is the guitar world equivalent of Bill Wilson and PO Ackley combined.)