Although I agree with Yu Zhang's answer, I'll propose another way to look at it: evil survives no matter what.
Chigurh represents a number of things; to me he is the personification of evil. No rhyme, no reason, no empathy, mostly random in the lives of the people he interacts with, causing suffering (and often death.) And it never stops. There's always evil in the world.
In traditional Westerns, the good guy wins in the end, and good triumphs over evil. This book/movie took that traditional setting to expose the randomness and pervasiveness of evil. None of the good guys win; at best they try to face evil courageously, and try to evade death for as long as they can knowing it waits for them no matter what.
It's interesting that the only time that Chigurh interacts with children is in the final scene he's in. It's not that kids are less selfish than adults (the adult at the border crossing wanted more money for his beer, and one of the kids wants to profit from Chigurh's injury as well) or more controllable. I think it represents that evil and death are present in lives even in an age of relative innocence. And if it doesn't get them then, it will someday.
The guy is unkillable. He gets shot, he gets hunted by strong men, he gets in a terrific accident, one that gives him a serious open fracture... and walks away, with just a little bit of cloth wrapped around his arm. *
Maybe I'm reading too much into it, but it seems to fit into the rest of the movie, how evil and senseless the modern world has become to the nostalgic sheriff.
*An open fracture isn't something he can fix, like digging a bullet out of himself. He'll need more than stolen antibiotics and almost-superhuman willpower. He will need a doctor. And I can't help but fear for the doctor who helps him.