Good question (which means I don’t know the answer for sure) – but I think the government will reimburse up to a certain amount of rent, so most people look for rentals that match the government’s payment (which is minimal).
I used to sell ads for the Reader and some of the rental ads had Section 8 wording. They were, for the most part, in the low-income part of town. It takes two-three years to get approved for Section 8 housing on the part of the tenants – not an easy process. Only those who truly need it end up getting it. Most people find a job before their approval comes in and thus, are no longer eligible.