I think the problem is more that society does not provide people with the knowledge of how to get out of poverty.
Another problem is that when we say "society", we generally mean someone else. It is about time that when people say "society", they include themselves in it. For most people, that is primarily just the offering of money to just causes, possibly some volunteer time.
But what we really need are more socially conscious entrepreneurs. Government's role should be to carve out a way for the market to be conducive to such people.

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"Man lives in the sunlit world of that which he believes to be reality. But unseen by most is an underworld, a place that is just as real... but not as brightly lit... A DARK SIDE!"
-opening from Tales From the Darkside