I'm not sure it's only stones that don't sell so well that are being dyed.
It may be more a case of finding more stones that can be dyed and dying them to sell more stones. Crazy lace agate has been sold for years and sells OK in it's natural form. Rock shops for year have sold slabs of it with bright dyed to use in lamps, wind chimes and inlaid in steps. Lately we've seen (and sold) a lot of blue dyed and red dyed crazy lace as beads.
Crazing and surface enhancement techniques have improved a lot since the days of cracking marbles in a frying pan. The cracked quartz, crazed magnesite in white and dyed colors and the surface enhancements that make "crab fire agate" so interesting are recent "improvements" to existing stones. (I'm not so sure they are really "improvements." to the stones.)
I'm told by some of the cutters that most of the dyes should not run on clothing and, if they do, it's because they were not dried enough before the were packed up. (Beads are usually dyed after cutting - as the last step before shipping.) I know there are different types of dyed that give the same colors. (Oil dye is much better than the water based dye for dyed coral, for example.) It would be a great improvement to my way of thinking if only permanent dyed were used. It's frustrating for a seller to have a batch of beads that are color fast and don't run and then get the next batch of the same stone and same color that DOES run. It's even more frustrating for the person wearing the beads on their new white blouse..
Washing questionable beads in warm soapy water is a good idea!