Japanese animated movie where a plague that turns people into stone spreads across the Earth

Question

I watched this animated movie 6 or 5 years ago.

It was about a spreading disease that turns humans into stone; it forced a company to make a project to freeze a bunch of people for 100 years in a castle hoping the disease will be gone by then. (I think they called it the "sleeping beauty project.")

The story follows two twin girls, a shy one and a more outgoing one; only the shy one had a ticket to get into the project. After they started the project they ended up waking up after only few days. They found the castle filled with monsters that killed most of them, leaving only 7 or 8 survivors.

The ones that I remember are the main character (the shy girl), a blond lady, a child (who liked playing with a game), a buff guy, a scientist and an old mean man. The survivors get attacked while trying to get out of the castle and most of them die, leaving the main character and the little boy as the only survivors in the end.

Answer 1

Probably King of Thorn (2005), adaptation of the 2002 manga Ibara no Ou.

Summary of the manga, from MyAnimeList:

Two twins, separated by fatal illness and a selective cure. Kasumi and her sister, Shizuku, were infected with the Medusa virus, which slowly turns the victim to stone. There is no cure, but of the two only Kasumi is selected to go into a sort of cryogenically frozen state along with 159 others until a cure is found. At some point in the undetermined future, Kasumi awakens to find herself and others who were in suspended animation in an unfamiliar world with violent monsters. Resolving to unlock the mysteries of her current situation and the fate of her twin sister, Kasumi struggles to survive in a treacherous world.

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Found with the Google query anime movie disease turn stone freeze site:myanimelist.net.