Welp. The oily stone is one of the things that keeps grabbing my attention on my latest reread. Might as well don the tinfoil. Most of which isn't new.

I'm not sure if the stone fell from space, but there's nothing pointing that it didn't either. From what I've noticed, the stone seems to have been left behind by someone or something ancient. How they got it or where did it come from? Who knows! BUT I do find it interesting the stone is scattered around Planetos in areas that eventually developed their own unique cultures.

Common factors between these separate cultures and the stone is that the stone is evil/foreboding, and that it's probably been around since the Long Night and (though not necessarily the cause of) the planet's magic and/or seasons. Since this is the stuff of legend, whatever made those structures could have left and died out, or they could have just disappeared after something happened. In stories, one of the more popular mechanics behind an intelligent civilization disappearing without a trace is that they found and/or experimented with something they probably shouldn't have. Since the maesters (apparently) believe that Planetos used to have normal seasons, something being released of such sheer magical or eldritch power that it royally fucks with the planet's seasons would probably have other effects on the planet, eventually (or immediately; who knows) resulting in a civilizations apparent disappearance as they went... wherever they went.

I know Lovecraft is one of GRRM's influences. Lovecraft's monsters often had aquatic characteristics, so the stone being carved into the shape of a kraken could be more of a direct hint, homage or what have you with whatever lore he has cooked up in his head. The idol on the Isle of Toads seemed like a more obvious nod to me, too. Aside from that, Lovecraft's work also often had to do with people stumbling upon knowledge we aren't meant to understand or use, often with those unfortunate to find it going batshit insane as a result and/or unleashing something.

On my reread, and now that I think of it, when Bran looks into the Heart of Winter in AGoT, I was reminded that whatever he sees terrifies him. He doesn't really describe what he sees at all, but if he "to the curtain of light at the end of the world, and then beyond that curtain," I'd expect he'd see shadow or something similar to our perception; going beyond that curtain to its opposition. Now, that dream would be a bit of a clusterfuck to do anything with beyond speculation. But since Asshai's oily stone seems unique in "drinking in the light," Asshai lies under the Shadow (of the Old Ones), because whatever happened there or in that general area resulted in messed up seasons and opposites facing each other (ice vs. fire, shadow vs. light, etc.).