China seems to have inherited this problem from the Russians.
You could say, Everyone seems to be caught between a ROK and a hard place. 
I have collected various articles on the topic and posted them here to give a broader understanding.
World Press - U.S. Warns China on N.Korea PolicyU.S. President Barack Obama is warning the United States may have to redeploy American forces in Asia unless China toughens its stance on North Korea.
A senior Obama administration official told The New York Times that Obama delivered that warning to Chinese President Hu Jintao this week during the two leaders' private dinner at the White House, just hours after Hu arrived in the United States.
According to the unidentified U.S. official, Obama said, if Beijing does not help curb North Korea's nuclear ambitions, the United States will have to realign its forces to protect against a possible North Korean strike on American soil.
U.S. officials have increasingly been warning that North Korea poses a direct threat to the United States. Obama is said to have raised the issue with Hu twice in recent weeks -- first during a telephone conversation last month, then again at their private White House meeting.
American officials told U.S. news outlets Friday that China appears to be taking the warning seriously. They credit renewed pressure from Beijing for the quick agreement on new high-level military talks between North and South Korea.
News.Antiwar.com Gates: North Korea Could Nuke USDefense Secretary Says Situation a 'Direct Threat'
by Jason Ditz, January 11, 2011
Citing North Korea’s continued effort to improve its not entirely effective long range missile program, Secretary of Defense Robert Gates predicted that not only would the nation have a “limited ability” to attack the continental United States within five years, but that they could use nuclear warheads when doing so.
Predictions of this sort are pretty common, and indeed two years ago the administration predicted that North Korea would have that capability in mid-2012. It seems US officials are forever more optimistic about North Korea’s ability to advance these programs than the North is, however.
The endless speculation centers around the Taepodong-2, a missile which has been in development since 1987. North Korea’s government has twice tested the missile, in 2006 and 2009, and it failed both times. US officials seem convinced enough of the missile’s viability, at least to the extent that it can be used to demand major funding of missile defense systems, which themselves don’t work particularly well, to shoot down the missiles on the off chance they ever get them working.
But Gates insists this proves North Korea poses a ‘direct threat’ to the US and that they must be “engaged” soon. Though he mentions negotiation the US has repeatedly rejected the notion of talks with the North Korean government.
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FoxNews - Nuclear push could bring North's collapse | SEOUL, South Korea –
Impoverished North Korea could bring its own collapse if it keeps pouring scarce national resources into its nuclear weapons program and military, a senior South Korean official warned in an interview to be broadcast Monday.
South Korean officials have used tough language against North Korea after two deadly attacks last year killed dozens of people. But it's still rare for a top Seoul official to speak publicly on a potential North Korean collapse and shows the South's growing impatience with its communist neighbor.
"I think they will come to the point where they can no longer sustain the burden of military expenditures," Chun Yung-woo told "PBS NewsHour," according to part of the interview posted on the U.S. public broadcaster's website.
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Chun is South Korea's chief presidential adviser on national security and foreign affairs and once was the South's top negotiator on now-stalled six-nation talks on the North's nuclear weapons program.
"They are already suffering from misery ... I think they will be worse off," Chun said. "I think their obsession with their military capabilities, especially weapons of mass destruction like nuclear weapons, chemical weapons ... that would be a short-cut to their demise."
He said "the energy for changing" North Korea is growing but declined to predict when that change might happen.
North Korea's state-controlled economy was devastated by natural disasters and mismanagement in the 1990s, and a botched 2009 currency reform and massive flooding last year are feared to have worsened it. However, experts say the North still devotes much of its scarce resources to its 1.2 million-member military under its "army-first" policy.
Read more:
http://www.foxnews.com/world/2011/01/17/skorea-nuclear-push-bring-norths-collapse/#ixzz1Bwl5SHVu
Background information from the CIA Factbook
| Disputes - international:
Risking arrest, imprisonment, and deportation, tens of thousands of North Koreans cross into China to escape famine, economic privation, and political oppression; North Korea and China dispute the sovereignty of certain islands in Yalu and Tumen rivers; Military Demarcation Line within the 4-km wide Demilitarized Zone has separated North from South Korea since 1953; periodic incidents in the Yellow Sea with South Korea which claims the Northern Limiting Line as a maritime boundary; North Korea supports South Korea in rejecting Japan's claim to Liancourt Rocks (Tok-do/Take-shima)
Refugees and internally displaced persons:
Trafficking in persons:
current situation: North Korea is a source country for men, women, and children trafficked for the purposes of forced labor and commercial sexual exploitation; the most common form of trafficking involves North Korean women and girls who cross the border into China voluntarily; additionally, North Korean women and girls are lured out of North Korea to escape poor social and economic conditions by the promise of food, jobs, and freedom, only to be forced into prostitution, marriage, or exploitative labor arrangements once in China tier rating: Tier 3 - North Korea does not fully comply with minimum standards for the elimination of trafficking and is not making significant efforts to do so; the government does not acknowledge the existence of human rights abuses in the country or recognize trafficking, either within the country or transnationally; North Korea has not ratified the 2000 UN TIP Protocol (2008)
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