I think that China has no interest in a nuclear-armed North Korea.
Koreans aren't fond of China and if North Korea doesn't need China to
survive that feeling might change policies to China's detriment.
Also, a
nuclear North Korea could easily prompt regional proliferation that
will dilute China's nuclear edge and partially nullify Chinese
conventional power.
Whether that means China is willing and able to stop
North Korea before we find ourselves at a hard decision point to strike
North Korea or accept North Korean nuclear ICBMs that can hit us is the
question.
I know some people say that China has an interest in North
Korea armed with nuclear missiles, and so it is foolish to think China will save us from resolving the problem.
But I think this conclusion conflates the current situation with China's past
glee at having North Korea pursuing nukes which rattled America, Japan, and South Korea. Reaching nuclear status is another thing altogether.