The process of becoming stonestruck is a phenomenon in wich a Demigod becomes stone after his divine energy exhausts. The more divinity a demigod has, the more time they can go without being stonestruck.
The child of two Noble Gods could survive for millennia, while the child of a God and a mortal can usually survive for a handful of centuries.
Before the Shattering and the Signature the mortals, those born without divinity, would be stonestruck immediately at birth. This was known as being Stoneborn.
While stonestruck, a demigod retains part of their conciouseness, as attested by priests and animists, and is possible to communicate with them if they are willing.
The Stone
The stone in wich the demigod transform is a curious substance: it cannot be broken or even moved, cannot melt or change in temperature. It is constant and immutable. These properties have induced some academics to hypotize that this stone is mado of the same substance of the Stillness.