Negative Income Tax (NIT)
  
Judging just by the name, this term could be the most popular public policy proposal in history. In fact, the way negative income tax works is very similar to how it sounds. An income tax that pays you. How do we vote for this?
Unfortunately, not everyone can receive an NIT...otherwise, the government would go broke pretty quick. Instead, it provides (in theory, anyway) payments to low-income people, instead of collecting taxes from them.
In many income-tax structures, there's a bracket with a zero-percent tax rate. Make less than x amount, and you don't owe anything in income tax. (The U.S. federal government got rid of the 0% bracket starting in 1987. In 1986, if a married couple filing jointly made less than $3,670, they didn't owe any income tax. They were probably living under a bridge...but they didn't have to worry about income taxes.)
A negative income tax adds a bracket below this: make less than a certain amount and the government sends you a check. As you've probably noticed, this doesn't exist in the U.S. It's more of an economic theory (a twist on the idea of a universal basic income) than a real-life program in practice anywhere.