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The Biden administration will be allowing asylum-seekers who were ordered to be deported for not attending their court hearings under the Trump-era “Remain-in-Mexico” program to enter the U.S. and re-start their proceedings here, according to a notice sent to Congress and obtained by CBS News.

Asylum-seekers whose cases were terminated will also be eligible for admission under this phase of the Biden administration’s draw down of the Remain-in-Mexico program, which required 70,000 non-Mexican migrants to wait outside the U.S. for their court hearings.

The Biden administration has already admitted more than 11,000 asylum-seekers who were previously required to wait in Mexico. The first phase benefited asylum-seekers with pending cases, like Lazaro, a political dissident from Cuba who was allowed to reunite with his U.S.-based wife and meet his baby daughter this spring.

Advocates have urged the Biden administration to expand processing to asylum applicants who were ordered deported under former President Trump’s presidency, arguing that many were not able to attend court appointments because of squalid conditions and high levels of crime in northern Mexico. Some asylum-seekers reported being kidnapped before their court dates.

More than 27,000 migrants subjected to the Remain-in-Mexico rules were ordered deported because they didn’t show up to their court hearings in the U.S., according to data compiled by Syracuse University’s Transactional Records Access Clearinghouse. About 6,600 asylum-seekers had their cases terminated.

It is unclear how many of those who qualify for the new phase of the admissions process will ultimately enter the U.S., as many migrants from Central America and other nations left northern Mexico after being sent there by the Trump administration.

“With these changes, thousands of people will finally be able to seek protection within the United States and leave the nightmare of the past several years behind them,” said Taylor Levy, an independent immigration attorney who assists asylum petitioners stranded in Mexico.

BuzzFeed News first reported in May that the Biden administration determined that those ordered deported for not showing up to their court appointments should have their cases reopened.

Those who are eligible to enter the U.S. have to register online through the United Nations refugee agency to receive an appointment to be admitted at selected ports of entry along the southern border. The U.S. has been testing these asylum-seekers for COVID-19 before admitting them.

Shortly after President Biden’s inauguration, the Department of Homeland Security stopped enrolling asylum-seekers in the Remain-in-Mexico program, which the Trump administration called the Migrant Protection Protocols, or MPP. 

Earlier this month, Homeland Security Secretary Alejandro Mayorkas formally terminated the MPP policy. In his termination memo, Mayorkas said “lack of stable access to housing, income, and safety” forced asylum-seekers in Mexico to abandon “potentially meritorious protection claims.”

“In deciding whether to maintain, modify, or terminate MPP, I have reflected on my own deeply held belief, which is shared throughout this Administration, that the United States is both a nation of laws and a nation of immigrants,” Mayorkas wrote in his memo.