Hundreds of migrant families who were separated at the border may have a second chance at seeking asylum in the United States after the federal government late Wednesday reached an agreement with those families’ legal representatives.

Under a now-reversed Trump administration practice, some 2,500 families were split at the U.S.-Mexico border, with many parents criminally charged for illegal entry and the children sent to government-contracted shelters. For months, those migrants and their advocates have claimed that these separations — and the anguish and anxiety they wrought — made it all but impossible for migrants to make the case that they should be allowed to seek refuge.

The first step in that process is demonstrating “credible fear” in an interview with an asylum officer. Dozens of separated parents have claimed they were unable to communicate their stories in that setting, distressed as they were over not knowing the whereabouts of their children. Still more parents said they agreed to be deported, waiving their rights to seek asylum, because they thought it would mean seeing their children sooner.

If the federal judge overseeing reunifications signs off on the new agreement, parents who failed their initial screening interviews and were ordered deported will have another chance to demonstrate their “credible fear” of returning to their home countries. If either parent or child passes that first screening step, they will be allowed to seek asylum together. This path was impossible under the family separation policy, which put parents’ and children’s asylum cases on separate legal tracks.

“The Trump administration will never be able to erase the full damage of its family separation policy, but this agreement is an important step toward restoring and protecting the asylum rights of impacted children and parents going forward,” said Lee Gelernt, the lead American Civil Liberties Union attorney on the reunifications case.

The agreement seems to do the least for parents who were deported without their children. It leaves open the possibility for some of those parents to return — but they will have to meet a high burden.

“The government does not intend to, nor does it agree to, return any removed parent to the United States or to facilitate any return of such removed parents,” government attorneys wrote in the document. But the government agreed to consider any “rare and unusual” cases flagged by those parents’ attorneys.