A S Byatt 
A Stone Woman (Storycuts) 

Following the death of her mother, an elderly woman begins to undergo a transfiguration. Her body grows flinty, toughens and crystallises. An Icelandic stonemason she meets in a graveyard becomes her sole confidant. As her inexorable metamorphosis continues, the stories he has to tell of his homeland and its legends begin to resonate.
Part of the Storycuts series, this short story was originally published in the collection Little Black Book of Stories.