It's about preventing the unification of Korea and allowing the US military to get closer to China's territory. That's a double loss as far as China is concerned strategically.
The situation has an easy solution. China collapses North Korea as it exists today and pays off all the military leadership (which actually runs the country); said military cabal gets to live in China, and doesn't get prosecuted for war crimes (all obvious requirements from their perspective). The US, South Korea and China put together an initial trillion dollar, 20 year, package for economic recovery. The US & South Korea agree to cede between 1/3 and 1/2 of North Korea to China, to be used as a form of territory buffer between the US / S.Korea and China. The US agrees not to position its troops any closer to Chinese territory (ie not to occupy any of the territory South Korea acquires), various rules could be put into place that everyone agrees upon to ease China's concerns.
This is a trivial problem to solve as far as the big problems of the past century go.
What's not trivial, is that North Korea's nuclear & missile technology is going to keep pushing forward, which will eventually spur the US / Russia / China to begin aggressively pushing their nuclear technology forward again. Further, North Korea will attempt to hand their nuclear technology to other nations, as there are no real consequences for them doing so (oh no, more sanctions), only the benefit of spreading nukes around further which lessens the spotlight on them.