It would still exist, but split into two blockchains. They would diverge, effectively becoming two completely different things, with different values. What kind

It would still exist, but split into two blockchains. They would diverge, effectively becoming two completely different things, with different values. What kind of asset you have would depend on what network you are connected to. This situation already exists for gold: gold (the physical stuff) in China and in the EU are loosely coupled: try to move your gold bar around.