Through decades of debate over illegal immigration, one group has been singled out for special protection. For the past 12 years, undocumented immigrants who arrived as children and grew up in the United States have enjoyed the ability to build careers and raise their own families without fear of deportation, thanks to the Deferred Action for Childhood Arrivals program, also known as DACA.

The program has persisted through three presidencies thanks to Congress’s failure to adopt a comprehensive immigration overhaul. But it has been under attack by Texas and six other Republican-led states for years, and may now be approaching its moment of greatest legal peril, having reached what is widely regarded as the most conservative appellate court in the country.

That court, the U.S. Court of Appeals for the Fifth Circuit, heard arguments on Thursday before a three-judge panel about whether to uphold a sweeping ruling by a trial court judge that would end DACA altogether.

The program was created by former President Barack Obama by executive action as a temporary fix until Congress passed legislation to address the fate of the Dreamers, as the group is known.

It has since proved hugely popular, enabling hundreds of thousands of beneficiaries to become employed at tech companies, universities and hospitals. Many have bought homes and paid taxes. At its peak, some 800,000 people were enrolled in DACA, a number that has more recently shrunk to about 500,000.

Former President Donald J. Trump moved to kill the program in 2017, one of a number of measures his administration took to try to reduce the number of undocumented immigrants in the country. The program has been suspended, reinstated and partly rolled back by court rulings ever since. Conservatives in Texas and other states filed the challenge now being heard in 2018.

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