Uh, hate to break it to you but EVERYBODY pays taxes. Sales tax, social security tax, medicare tax.
Nearly everybody pays state and federal tax. Sure, the absolute most destitute subsisting on crumbs no indoor plumbing living in a trailer poor pay nothing, but poor is a spectrum. And there are people who are poor who pay, albeit a little, state and federal taxes. If I recall, making up to $14k per year puts you in the 10% bracket. That's poor, and if you haven't any children or mortgage payments, you're paying 10% of your pitiful income to the fed. And something less to the state.
Not every poor person is the evil "welfare queen" stereotype with twenty kids and a huge amount of deductions. Believe it or not, there are folks who are (a) poor and (b) pay some money in state and federal income taxes. The guy that empties my office trash can, for example, springs to mind.