After seeing this question on the number of kyber crystals in the Death Star, I would like to know if any of it survived the destruction as rubble (as per the Alderaan asteroid field).
There must have been some solid debris from the explosion(s) -- both the original and remastered destruction scenes show small incandescent fragments, rather than just an expanding cloud of star-hot gas.
Whether any of the kyber crystals from the main weapon survived seems pretty unlikely. The main weapon was connected directly to the power reactor that exploded in both Death Stars, which strongly implies a potential power surge to the weapon that would rival a small supernova (given the weapon, in normal operation, was capable of blasting a planet apart energetically enough for most of the debris to escape its own combined gravity well). I'd be very surprised if anything material could survive that kind of power surge through the system that was designed to feed it stellar-level power in the first place.