Indiana may not have one of the largest populations of illegal immigrants in the country, Thomas said, but they tend to be concentrated in rural areas where they work on farms.

Those places are also where "welfare" programs like Medicaid still carry shame, she said.

"So it's a double dose of stigma," she said. "The place you go to apply for a benefit is the local office of (the Indiana Family and Social Services Administration). In your community, in these small rural towns, everyone knows everyone.

"If you walk in that door, the chances are your neighbor or your neighbor's husband or wife, someone in that office, knows who you are or you may be related to them. There's just a whole lot of stigma attached."

Locally, HealthLinc — a safety-net medical clinic with locations including Valparaiso, East Chicago and Michigan City — had its number of uninsured kids decrease from 543 in 2016 to 390 in 2017, but then rise to 591 last year, according to Executive Director Beth Wrobel.

Northshore Health Centers CEO Jan Wilson said about 9 percent of the children her clinics (in Portage, Lake Station, Chesterton, Merrillville and Hammond) serve are uninsured, a rate that has remained fairly steady over the years.