The first sentence might be rewritten like this...
His heart failed his body.
The second sentence could be rewritten like this...
Aspects of the U.S. are now so poisonous to the body politic that they are on the verge of collapse.
But it sounds like you're looking for a single, unifying word. In fact, people who are suffering from defective organs or illnesses are often said to eventually collapse. The lungs, in particular, can collapse, and one might say the respiratory or circulatory system collapsed.
The term Achilles heel also comes to mind. One might say, "The United States collapsed after virtually every major institution had succumbed to corruption, but the nation's Achilles heel turned out to be the education system, which nurtured citizens too ignorant to fight back."
P.S. It's kind of lame, but the term weakest link is also worth considering.