More than 99% of illegal immigrants caught and released a year ago as part of a special border “parole” program are still at large, according to new government data that signal just how difficult it will be to unwind the millions of migrants who have gained a foothold under President Biden.

The migrants are a critical test case for the Biden administration, with a federal judge demanding unprecedented transparency in how Homeland Security is handling the 2,572 people.

All of them were supposed to have reported in by last summer, but according to new data filed with the judge at the one-year mark, 25 still hadn’t checked in with U.S. Immigration and Customs Enforcement.

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ICE, meanwhile, has failed to issue an immigration court summons to 340 others, meaning that a year on, they’re still not in deportation proceedings.

And ICE said it can confirm the deportation, departure or death of just 14 people, meaning 99.5% of all of the migrants caught and released under this parole program are still believed to be here. Only one of the migrants was being held at the time ICE reported to the court in late May.

Andrew “Art” Arthur, a former immigration judge, said the migrants epitomize the problems Mr. Biden’s administration has had.

“Those 2,572 people are not even just a case study in Biden immigration enforcement, they are the Biosphere 2 of Biden immigration enforcement,” he said.

“It is a high-profile case with a judge that is laser-focused on DHS’s immigration enforcement efforts and yet they still can’t do what Congress said they are supposed to do,” Mr. Arthur said.

ICE didn’t respond to inquiries for this story.

Judge T. Kent Wetherell II ordered ICE to report on the migrants after the government released them in contradiction to his order last year halting the Border Patrol’s parole program.

Homeland Security released them without an immigration court date but told them they needed to check in with the department within 60 days to collect a court summons, or Notice to Appear (NTA). That is what officially starts deportation proceedings.

More than 40% of the migrants violated the 60-day check-in, and even more had yet to be served an NTA.

Under prodding from Judge Wetherell, ICE managed to get more check-ins and serve more NTAs, but the latest filing underscores just how much trouble the agency has had in tracking them all down.

Even though more than 300 migrants remain free without an NTA, ICE managed to serve just one new summons over the month preceding the latest report.

One other migrant filed an asylum application with U.S. Citizenship and Immigration Services.

“The individual was not detained, and an NTA was not served,” Marc A. Rapp, a senior ICE official, told Judge Wetherell.

The parole migrants are now part of a total backlog of some 7 million people ICE has in its deportation system.

Some have already been ordered removed and are defying those orders, while others are still awaiting final court decisions.

In 2018, ICE’s docket stood at just 2.6 million and at the end of fiscal 2020, toward the end of the Trump administration, it was still just 3.3 million.

The growth since largely reflects the border chaos under President Biden.

After more than three years, Mr. Biden took new decisive steps earlier this month with a new policy intended to severely limit asylum claims, which have become the loophole illegal immigrants use to win a quick catch-and-release.

Immigration advocates have sued to stop the policy but it remains in effect for now — and Homeland Security officials say it’s working.

They report that Border Patrol apprehensions are down 10% and they expect that figure to increase as would-be migrants alter their plans.

But even if the border is solved, unwinding the years of chaos will be a gargantuan challenge.

Like the test group that Judge Wetherell is monitoring, many of the catch-and-release migrants under Mr. Biden were set free under “parole.” That is a special power of the Homeland Security secretary, which is supposed to be exercised only in unusual instances where a major U.S. interest or special humanitarian case is involved.

Experts say Secretary Alejandro Mayorkas has used it in millions of cases, and they say the ouster rates for them are likely no better than for the test group in Judge Wetherell’s case.

The test group migrants demonstrate the breadth of nationalities arriving at the southern border, with nearly four dozen countries represented.

Some 22% of them were Venezuelan, 17% were Colombian and 14% were Peruvian. But there were also people from Somalia, Kazakhstan, Afghanistan, Uzbekistan and Ghana.

Among the 25 who have yet to check in are 10 Venezuelans, seven Guatemalans, three Hondurans, two Salvadorans, two Peruvians and one Ecuadorian.

Venezuelans make up more than a third of the migrants who have yet to be served an NTA, with Colombians and Indians ranking second and third. Others on the list include Chinese, Georgians, Angolans, Nepalese and Senegalese.