This concept is used in Windaria and an early episode of Pokémon (Episode 20: "The Ghost of Maiden's Peak").
Did it come from a Japanese legend I'm not familiar with, did it come from the Windaria novel, or is it just a Kunihiko Yuyama thing?
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Stone legends are indeed pretty common just as TurkeyFried stated. Most of these are based on Loyalty towards a person ( most common in anime waiting for a loved one)
It is said that the petrifaction version originate's from Vietnam
Hòn Vọng Phu (Statue of Husband Waiting)
But now a days in tv shows and such they give their own meaning to it and reasoning
You can check this out for some more example's of this phenomena