Washington (CNN) The Trump administration is releasing its plan for putting back together the thousands of families it separated at the border -- but the reunions won't happen quickly.

In a release Saturday night, the Departments of Homeland Security and Health and Human Services said 2,053 children were still in the custody of HHS and awaiting being returned to their parents.

Under the plan, however, those children will keep waiting in custody, with reunifications only happening once the parents' deportation proceedings are completed. The families will either be reunited before deportation or, if the parent is released from detention, after the parent applies to serve as the child's sponsor under HHS rules.

As part of the reunification effort, the government is building out better organized databases linking the parent and children's information and whereabouts and working to better facilitate communication between them, the fact sheet said.

The guidance came days after President Donald Trump abruptly reversed course on his administration's decision to refer all adults caught crossing the border illegally for prosecution, including those with children -- a decision that resulted in more 2,500 children being taken away from their parents in the almost two months it was in place.

DHS said that 522 had been reunited since the policy began, with 16 more reunions in process delayed due to weather.

But Trump's executive order on Wednesday telling his administration to keep families together only added to the confusion at first -- as the order seemed impossible to actually put in place. In the wake of the order, guidance obtained by CNN showed that the US Border Patrol would stop referring parents for prosecution until further notice.

The move follows days of fallout caused by the President's reversal, which happened suddenly. Thursday into Friday, officials across the administration huddled intensely within agencies and across agencies trying to work out how, exactly, the order would be implemented.

On Friday, DHS had already reunited any children that were still in its custody with their parents -- a smaller group that had likely been separated within the last three days and had yet to be transferred to HHS care. But the future of the thousands already affected remained in limbo.

Under the plan, children will be reunited with their parents based on the result of their parents' immigration proceedings. In the meantime, parents will continue to be detained by Immigration and Customs Enforcement pending an immigration judge's decision on their right to stay in the US, and the children will remain with HHS. Keeping the adult detained means their immigration court case moves more quickly.

If a judge decides that the immigrant may have a claim to pursue and the immigrant is deemed eligible for release, the parent can apply as a sponsor for their child in HHS custody. This is required by law once the child is in HHS custody, and the sponsorship application process can take weeks, though it's unclear whether the parent can start that process before they are released from detention.

If a judge decides that the adult is eligible for deportation, the child will be reunited with the parent prior their deportation from the country.

In its release, DHS noted that it is the parents' choice whether to be deported with their child, and that "in the past many parents have elected to be removed without their children."

It's still unclear who will take responsibility for linking parents with children.

Policies to date have put the onus on parents to track their children down using an HHS hotline, which parents and the lawyers and case workers working with them described as confusing and often ineffective. The fact sheet says ICE and HHS will work to facilitate communication, but still lists numbers that parents should call for assistance.

When the prosecution policy went into effect, HHS became the natural place for the children separated from their parents, as under existing laws the agency cares for undocumented minors who enter the country illegally by themselves.

Children in the system

But to hand the children over, they were essentially redefined as unaccompanied migrant children -- subjecting them to the same HHS procedures as children who entered alone.

That meant that their cases, tracking information and the agency that was caring for them was completely separate from the organization caring for their parents -- and no planning appeared to have gone into how the families would be reunited.

In recent days, ICE has been standing up its new reunification center at Port Isabel Service Processing Center in Texas, but the focus of that center is reuniting parents who are ready to be deported back to their home countries.

Though criminal charges for the misdemeanor offense of crossing the border illegally take only a few days to resolve and the immigrants are usually only sentenced to time served, by the time parents emerged from Department of Justice custody, their children had already been sent to shelters elsewhere in the country.

Parents and their representatives have been left struggling to find out where the children went, and because of secretive procedures protecting children in government custody due to privacy concerns, there is no straightforward way to look up a child in the system. Parents have been given hotline numbers to call that users describe as byzantine and hard to get through.

Also, once children are in HHS custody, procedures require that they be released to someone who qualifies as a "sponsor" under the agency's policies, which would almost certainly exclude an adult in DHS detention facilities, meaning parents can't be reunited until the government decides to release them or deport them.

None of the agencies involved in the process have been designated as the central keeper of both parents' and children's data with the responsibility of putting them back together at the end.

The process to find one's child is "incredibly challenging, and what I fear is that it might, in some cases, be impossible," said Wendy Young, president of the advocacy and legal support organization Kids in Need of Defense and an immigration policy expert.