Given how strange the circumstances are, we'll say there can be some flexibility in whether pieces that have broken off stick around after recovery/dissipation. Pieces that have broken off (or the shattered corpse in the case of a dissipation) can stick around as permanent petrified objects if the player wills it, but it will be up to them whether other characters are allowed to keep those trophies or whether they disappear, either in whole or in part.