From what I recall, there are plans in place for such occurrences, negotiated between the US and China, in case of the regime destabilizing. China really REALLY doesn't want to deal with the problems of the NK populace, but they equally don't want a close US ally on their border in the form of SK. Because without such plans, the armies of the US and China would pretty quickly meet in the middle, mistakes would be made, resulting in large scale friendly fire at the very least, and possibly world-ending nuclear war. And of course there's the NK nuclear weapons which would need to be secured by spec ops from both nations immediately. So NK would be split down the middle by China and the US. The US would probably cede their chunk to SK; what China would do would heavily depend on their diplomatic strategy du jour.
If they were trying to turn SK to their own favor, they might just cede the entire thing to them; though that's highly unlikely.
Since they really don't want to deal with the NK populace, I suspect they would give most of it to SK, then keep a nice, thick chunk along their border and militarize the hell out of it. They would then send any refugees/inhabitants into the SK part, and let them deal with the mess. Possibly while kicking back and munching on some popcorn. It'll take an entire generation, maybe two, to rehabilitate the region; which is why China's biggest goal is preventing a massive wave of NK refugees flooding over their border.