Appearently yes, welfare does breed poverty.
http://www.fee.org/vnews.php?nid=3741
Another way of determining whether the poor have benefited from income growth is to look at changes in the percentage of families classified as living in poverty over time. By our current definition of poverty, 56 percent of families in the United States were poor in 1900. By 1947, even after the economic shocks of the Great Depression and World War II, the percentage of families in poverty had been reduced by more than half, to 27 percent. By 1967, the percentage was halved again, to 13 percent. Notably, the decrease in poverty between 1900 and 1967 occurred before the advent of the greatly expanded welfare state. In other words, it was the free market, not government welfare, that caused the poverty rate to fall from 56 percent in 1900 to 13 percent in 1967.