Typically ex jewelry stones are damaged if they are color or CZ. Diamonds are worth pulling depending on size. Diamond market is Weak right now....very week. I have buyers but I am holding out. I do stone return if its just a few. Expect anywhere from $10 to $40 per karat on junk diamonds from wholesalers.
Most of them get sent back to India where kids chained to benches sort them back into salable lots in order to pay for there $15-$50 in vaccination or medical debts, Typically this debt may take a year or two to pay off. The diamonds are then sent to china, reset into rings, and over priced sold on home shopping network to rednecks only to be scrapped out a few months later at %10 on the dollar at cash for gold to buy cigarettes....repeat process...no I am not kidding.
Chemical getting the stones out is the safest way, I have seen more things damaged by people trying to grind, cut etc, Plus they lose gold grinding, to remove stones. When most refiners do stone return for free if you ask, or charge a very small fee.
Obviously prongs can be pulled back. But channel set stones, pressure set etc. safest way to extract them...Full chemical assay.