From Always Sunny in Philadelphia:

  Mac: Unemployment runs out, what are you gonna do then?
  Dennis: Well then we'll just go on welfare.
  Mac: Welfare is for people who need it, like drug addicts
  and single mothers. It's not for over-privileged pieces of
  shit who want to waste millions in taxpayer dollars...

Basically, 1) unemployment runs out; 2) it's difficult to get welfare unless you have children or have a disability, and being classified as disabled is more difficult than commonly believed, especially for younger people, even though it sometimes seems like every idle soul is drawing a disability check; and 3) since the Clinton-era reforms many welfare programs have a lifetime cap.

FWIW, unemployment can pay better than minimum wage because unemployment is usually paid as a percentage of your earnings. But you'd need to have been making substantially more than minimum wage.

Also, a lot of social programs are pretty good about proportionally cutting back on benefits as income grows. It's still a real problem with some programs (there are many, and they're byzantine), but I think it's exaggerated somewhat. It's like "write-offs" for taxes--most people have no understanding of them, and believe they function far differently than they do in reality. To quote another one of my favorite shows:

  Kramer: "It's a write-off for them."
  Jerry: "How is it a write-off?"
  Kramer: "They just write it off."
  Jerry: "Write it off what?"
  Kramer: "Jerry, all these big companies, they write off everything."
  Jerry: "You don't even know what a write-off is, do you?"
  Kramer: "No, I don't. But they do. And they're the ones writing it off."