(CNN) Immigrant advocacy groups are gearing up to track down more than 400 parents who were separated from their children and deported without them.
The challenge is so daunting that government attorneys have bristled every time it's come up in court.
And now a number of nonprofit groups say they're prepared to join in a massive search.
"It's going to be really hard detective work," said Lee Gelernt, an American Civil Liberties Union attorney who's been leading the organization's lawsuit over separated families.
Already, some devastated parents are coming forward, desperate to be reunited with their kids, according to advocacy groups. But there are hundreds whose whereabouts are unknown.
Here's a look at some of the key issues at play -- and major hurdles complicating the process:
According to the latest government statistics, some 430 parents from separated families were likely deported without their kids. Officials maintain that before that happened, the parents consented.
"Parents that did return home without their child did so after being provided an opportunity to have that child accompany them on the way home," said Matthew Albence, who heads US Immigration and Customs Enforcement's removal operations.
"We cannot force a parent to take a child with them," he added.
It's true that some parents do make the harrowing choice to be deported without their kids; they may decide it's the best option for their families -- and the only way for their children to survive.
But the ACLU and other immigrant rights groups argue that parents were coerced into signing paperwork they didn't understand.
"It is our position that all of those families need to be considered as families that should be reunified and that the government should reunify them," said Michelle Brané, director of migrant rights and justice for the Women's Refugee Commission.
That's a point of dispute that's likely to come up when ACLU and government attorneys appear in court again on Friday. No matter what officials say, immigrant advocacy organizations say they're determined to track down all the deported parents to verify details of their cases.
"Our hope is to find each one of those (parents) and find exactly what happened and why are they not with their child and do they want that child back," the ACLU's Gelernt said.
Finding deported parents will be much easier said than done. Gelernt described it as an "enormous task."
Why?
A number of factors could make parents afraid to come forward, says Lisa Frydman, vice president of regional and policy initiatives for Kids in Need of Defense. The organization announced Thursday it was launching a new initiative to help reunite children with parents who were deported. The project will involve outreach efforts aimed at finding hundreds of parents in Central America, including working with local governments and community groups. But Frydman said the organization is still pinpointing what steps to take.
But some parents, advocates said, came to the United States in the first place because they were fleeing dangerous circumstances and feared persecution in their home countries -- at times at the hands of local officials and governments. After they're deported, they may resettle in a different part of their home country and not want their whereabouts known.
That, Frydman said, means some parents who want to be reunited with their kids still might not speak up.
"They feel extremely afraid for their life to come forward and seek assistance and be labeled as somebody who's been deported ... or as a potential refugee," Frydman said.
Even after parents are found, advocacy organizations say there will be much more work to be done.
It's complicated to deport anyone from the United States -- particularly so-called unaccompanied minors, which is how officials have been categorizing kids from separated families who are still in custody, including those whose parents are no longer in the US.
The process requires coordination between multiple government agencies and many steps, including acquiring travel documents and plane tickets.
"All of those factors can take time," Frydman said. "And that's in the most straightforward of cases."
Another option could be on the table: A judge could order some parents to be brought back to the United States.
"If something was erroneous in their deportation, they would have the right to come back and a judge can order that," Gelernt said, "but I think that's going to have to proceed on a case-by-case basis."
For organizations that help deported migrants readjust to life in Central America, seeing parents deported without their kids isn't a new phenomenon, Frydman said, but it's been on the rise. And parents have been reaching out to Kids in Need of Defense and the organization's partners in the region.
"The parents in country post-deportation are very confused, really afraid, don't know if they're ever going to get their child back and don't know what to do to get their child back," Frydman said.
Silvia Veronica Raquec Cum, who works with deported migrants in Guatemala, said she's seen the situation take a devastating toll.
"The parents are in a very bad state emotionally," she said.
In one recent case, she said, frantic parents who reached out to her organization were relieved to learn that their 6-year-old son was in a shelter in Arizona. They spoke with him several times on the phone. But the last time they called, the boy told his parents he didn't want to speak with them anymore.
Now the parents, she said, are terrified that something's happened to their son.
"They said they can't sleep or eat," Raquec said.
All they can do is wait for answers from thousands of miles away. And it could be months before they get them.
"It's neither a day nor a week. We don't want to get their hopes up," she said. "We tell them it's a long process."