Also, the US helps the South Korea military (and previously, its economy). I believe there is a clause in the constitution where in the case of a full scale war, a US general will assume command of all the military forces of the South
http://en.wikipedia.org/wiki/Korean_War [1]
Here is an interesting read: http://en.wikipedia.org/wiki/Division_of_Korea
Beijing - Pyongyang is merely 800Km, after all.
Before North Korea had a nuclear weapon, much less the ability to build numerous of them, China propped up North Korea in countless ways for decades (from food to weapons to moral support). China could have very trivially killed Kim (or requested his overthrow), with absolutely no consequences. It's not like the weak and vastly smaller North Korean army was going to invade China, particularly after the Kims were gone.
I believe China could still dismantle North Korea. I think their fear is the chaos that could follow, from millions of refuges to perhaps a new military dictatorship to loose nukes.
There's a more practical reason for them to hope the regime doesn't fall: it creates a refugee crisis on their border and the CCP governance model is 'stability uber alles'.
Kim Jong-Un may be about to find that his sponsor's patience is neither unconditional nor unlimited. The Chinese leaders are not stupid. They know they have a problem.
The best endgame for Kim is an offer of exile in China, at this point. That may be what he is fishing for here.
Considering what would happen if the borders to China were opened, I think it would be a huge humanitarian situation.
http://en.wikipedia.org/wiki/Korean_war
should give you some background.