When the petrification meter is filled, the player will be turned to stone. This is equivalent to dying. You will lose all souls, be turned hollow and return to the last bonfire at which you rested.
Petrification can be inflicted on the player by a few enemies, including Basilisks, Aldia's Keep Kobolds and others. Players turned to stone can be seen in stone form, much like bloodstains, in other players' worlds.