Undocumented immigrants are ineligible for many public benefits. And Texas offers fewer than most states.

Edna Yang of American Gateways, an immigration legal services provider in Texas, said that undocumented immigrants in the state qualified for only a small number of benefits, including emergency medical services, food aid for children and public education.

The governor’s office has said that the cost of each additional student enrolled in Texas public schools is about $6,100 per year, not including the cost of providing bilingual and special education services, which add more than $2,000 in additional spending.

The last time the state’s comptroller studied the issue was in 2006. The report found that while undocumented children cost about $1 billion to educate at the time, unauthorized migration into the state had an overall positive effect on the Texas economy. Mr. Huennekens, of the immigration reform group, said the state’s programs for students with limited English proficiency cost more than $7 billion in 2016.

But barring undocumented students could upend the system for everyone, said Zeph Capo, the president of Texas AFT, a teachers’ union, who said schools could lose the per-pupil state funding that accompanies those students as well as the additional money sent by the federal government. “All undocumented kids are not all in one school or in one school district,” he said. “It’s going to hurt everybody.”

Attitudes about immigration have shifted in Texas, where former Republican governors like George W. Bush and Rick Perry adopted relatively moderate tones. Mr. Perry, during his term, signed a law allowing undocumented college students access to in-state tuition and financial aid at public universities in Texas.

But taking a hard stance on immigration has been a politically comfortable place for Mr. Abbott. He used the issue to beat back challengers in the Republican primary, and has returned to it in his general election contest against Beto O’Rourke, the Democrat and former congressman from El Paso.