In the real world there are cases where a person with 0 income get's X support from the government. On the other hand there are people with income less than X who don't get government support.

That means there an incentive out there to have income 0. The phrase "paying for" suggests to me that you create a monetary incentive for something.

I think you dilute the value of the phrase "paying for" when you don't let it mean "create a monetary incentive for something".