Timing is everything.
Although, I'd doubt they'd just "die". More likely, it would be the kickoff to a new world war. They aren't going to go quietly.
This is another reason why "managed" solutions to energy are more-than-likely a big mistake. The carbon regulation crowd would love it if we could just turn it off overnight. That would be disastrous not only for the world's consumers, but even more so than these producing countries that produce little else. It will take decades, if not a century to adjust in a stable manner.