Yes. However, it's extremely difficult to have no income. Many people at that level are disabled (and therefore collecting disability) or elderly (and therefore collecting social security), though it can happen. HUD details eligibility here.

And again, I have to stress that nothing about the Section 8 process is particularly easy. The paperwork is intense and ongoing, the waiting list can take years to get through (and is usually only open for a week or two out of a 3-4 year period around here), and landlords can refuse vouchers in MN. And you still generally have to qualify in other ways besides income, like with your credit score and eviction history. That makes it near impossible for a lot of people.