Sorry, but I have to call total BS on those claims. This high school third-hand gossip doesn't stand up to actual data.
Perhaps you missed the 1996 Welfare Reform Act, which put a time and money limit on welfare benefits and forced recipients to find jobs?
Here is a snippet from a USA Today article called "How welfare reform changed America" (emphasis added):
KANSAS CITY, Mo. — Michelle Gordon was 30, a poor, single mother with four kids between 5 and 13, when the federal government decided in 1996 that parents on welfare should go to work.
Since then, Gordon's life has been "a little bit of a roller coaster." She has held about 10 jobs — at a call center, as a nurse's aide, as a janitorial supervisor, most recently at a grocery store. She lost that job on April 19, her 40th birthday. It took her two months to find another. For 25 hours a week, she cleans bathrooms and vacuums floors at a drug rehabilitation center.
[...]
The law, signed by President Clinton on Aug. 22, 1996, has transformed the way the nation helps its neediest citizens. Gone is the promise of a government check for parents raising children in poverty. In its place are 50 state programs to help those parents get jobs.
In the 12 years since caseloads peaked at 5.1 million families in 1994, millions have left the welfare rolls for low-paying jobs. Nearly 1 million more have been kicked off for not following states' rules or have used up all the benefits they're allowed under time limits. Today, 1.9 million families get cash benefits; in one-third of them, only the children qualify for aid.
So as of this 2006 article, fewer than 2 million families were getting welfare benefits. In a country of over 300 million people, that's a tiny percentage of the whole, probably less than 1%.
"The DNA of fictional populations appears to be the most susceptible to extinction." - Simon Southerton