Some of the bills are just written off as bad debt. Essentially thrown away. But in many cases the hospital back office will work to get indigent patients enrolled in Medicaid and then send the bills to the state government.
It's someone looking at the EMTALA requirement for emergency departments to provide stabilization without regard to ability to pay without also realizing that the US has public health insurance for the medically indigent.
Effectively it is no cost care for those who are sufficiently poor.