The lore is that Kyurem came from the sky long ago... What if, this actually happened when the Original Dragon split?
Kyurem is the absence of Yin and Yang. By Reshiram and Zekrom splitting, there ceased to be a being representing such a thing, as they became separate beings.
So Kyurem would've been born as a byproduct of the split, but not as the remains of something that was ever there.
Now... that Kyurem merges with either Yin and Yang, it could represent which of either of the boundaries it, as "wuji", reaches. My theory on it is, that if the three of them were to come together, Kyurem would become some sort of true opposite to the Original Dragon, that encompassed everything beyond both boundaries.
As for the God stone... it seems it would've matched Kyurem, but, it obviously doesn't have Kyurem inside it nor its spirit nor anything, so who knows. It wasn't used in Black and White though, so unless it is used in Black and White 2 speculating what would be inside it is like speculating what's inside the GS Ball.