Well, no they don't, and no they're not. In fact, as Walter Williams says in a recent column, most of today's rich are yesterday's poor. For the most part, 'the poor' don't want to stay that way, and they haven't - it's them that's mostly busy getting richer, with about 80% of American millionaires being first-generation wealthy.
Furthermore, 'the former poor' are making themselves rich, and in that sense only can you say they're getting rich off the backs of the poor - it's their own back. Thomas Sowell argues:
Are there genuinely poor people who stay poor? Yes. However grossly exaggerated the numbers, there are such people. But studies that follow the same individuals over time find that most of those in the bottom 20 percent of income earners are also in the top 20 percent at some other time in their careers....And 'social justice' mostly harms not helps the poor because it calcifies the social structure and the economy into present patterns. Sowell's new book 'Black Rednecks and White Liberals' argues that for example American "ghettos are still filled with 'black rednecks' who have never escaped [their] self-destructive patterns. Why not? Their attempt to escape, Sowell says, has been consistently and repeatedly hampered by white liberals!" The 'black redneck's' have still got what Malcolm X called 'their slave minds'; the 'white liberals' want them to keep it because there's votes and kudos in being patronising.
There was a time when you could legitimately contrast the idle rich and the working poor. But that time is long gone. Nevertheless, the image is still politically useful, so you are likely to see that image invoked again and again by candidates practicing divide and conquer politics, sometimes known as class warfare or by its more fashionable name, 'social justice.'
See for example the Labour Party manifesto.
As Reverend Ike always says, "The best thing you can do for the poor is not to become one." Right on, Reverend. If Bishop Tamaki talked like that I could be a fan. Pity he's just another fascist arsehole with a power complex.
And forget about the so-called 'gap' between rich and poor. The richer the rich are, the bigger the gap. And the richer the we're all allowed to get, the easier for the poor to become rich and to stay that way. PJ O'Rourke sums it up in his classic book 'Eat the Rich',
If we want the whole world to be rich, we need to start loving wealth. In the difference between poverty and plenty, the problem is the poverty and not the difference. Wealth is good. ... wealth is not a world-wide round-robin of purse snatching... [T]he thing that makes you rich doesn't make me poor. ... Without Productivity, there wouldn't be any economics, or any economic thinking, good or bad, or any pizza, or anything else. We would sit around and stare at rocks, and maybe later have some for dinner. ... Wealth is based on productivity, and productivity is expandable. In fact, productivity is fabulously expandable.Productivity is good. So is getting rich - if only governments and those white liberals would let us.