(CNN) Migrant women waiting to be reunited with their children have been held in legal limbo for days, technically "released" from ICE custody but not allowed to leave, immigration attorneys and witnesses tell CNN.

Multiple female detainees at the Port Isabel Detention Center, near the southern tip of Texas, have been officially processed for release but continue to be held without explanation at the facility, according to immigration attorneys and witnesses.

The accounts from inside the ICE-run facility in Los Fresnos, Texas, include women who say that for days they have only been given bread to eat while they wait to be reunited with their children. Others have said the food is adequate.

The women have been moved to a separate barracks where they wait in civilian clothing, officially released but not allowed leave, according to attorneys and witnesses.

"They just tell us 'soon, soon, soon' when we ask if we'll be able to talk to our children," a Port Isabel detainee named Carol told CNN in a phone call on Sunday. She asked that we not use her full name.

Carol, 30, told CNN she has been at Port Isabel since crossing into the country illegally from Honduras on June 2. Conditions at the detention center, she says, have become incrementally worse over the last two months.

"Where they're holding us to be processed is freezing. It's so cold some of us are having trouble breathing," she says.

Carol says her 7-year-old son is being held in the Cayuga Centers, a nonprofit in New York where many migrant children have been detained while they wait to be reunited with their parents.

The government's response

Hundreds of parents are in the process of being reunited with children that the government took from them at the border. Some of the families have been separated for weeks or months. A federal judge in California has ordered that separated families in immigration detention be reunited by Thursday.

The strange limbo seems to be a function of the hurried effort to reunite more than 2,500 children in government custody by the Thursday deadline after they were identified with roughly two weeks to go.

Immigration and Customs Enforcement (ICE), which manages the detention centers, and Health and Human Services, which cares for the separated children, did not fully explain to CNN after multiple inquiries why these women would be waiting in this transitional state for so long. Nor did they respond to the allegations about the conditions.

In a statement provided to CNN by ICE spokeswoman Sarah Rodriguez, the agency referenced "logistical challenges" presented by large-scale transfers. She also said the agencies were prioritizing the children's wellbeing.

"DHS and HHS are working tirelessly to reunite parents and children within the court ordered timeline," the statement said.

"In order to facilitate more efficient reunification of family units going forward, ICE has leveraged additional resources to enhance processing capacity for adults/parents held in the Port Isabel Detention Center (PIDC). The safety and well-being of children remains our top priority as we work to comply with the court's order as expeditiously as possible."

While the statement did not address some of the specific concerns raised by attorneys and witnesses at PIDC, it added that "on average" most children brought to PIDC for transfer to DHS custody by HHS are "reunified with their parents within a few hours of their arrival."

An ICE official acknowledged that from July 15 to 16 there were some children who had to sleep in the Port Isabel Detention Center overnight. That facility is not a family detention center, so children are not supposed to stay there that long. Since then, the official said, ICE has ensured no child has spent more than a few hours waiting to be reunited with their parents.

Attorney: My clients feel like they're 'being held hostage'

Government attorneys and officials have said in court that once a child and parent are both cleared for release, their reunion should happen within a day or two at most. But the reunions do not seem to be occurring as planned.

In at least one case, a woman who was processed for release on Wednesday still had not been released as of Monday morning, according to immigration attorney Eileen Blessinger. The woman spoke with CNN on Wednesday and said she had been told she would be reunited with her young son that day.

Other immigration attorneys recounted similar stories.

Immigration attorney Thelma Garcia says her clients feel as though they are "being held hostage."

Garcia told CNN one of her clients inside Port Isabel told her, "I have not spoken to my child in almost two weeks." According to Garcia, the client also said, "the phones don't work here where we are at."

Multiple female detainees have told their attorneys or CNN that in their transitional state, they no longer have ways to communicate with the outside world.

Garcia's client was moved to a holding barracks at PIDC and was told that her 14-year-old son was only 40 minutes away at a shelter and that they would be reunited. The client told Garcia she is still waiting.

"There's no word yet on when the reunion will happen," Garcia told CNN.

Attorney Abiel Garcia says his clients have also been kept in limbo.

"We were able to meet with [our client] on Friday and she was in civilian clothing. But as of today, she is still being held at the detention center, though she has been processed for release," Abiel Garcia told CNN Sunday evening.

"It's shocking to see this happening when parents were already being released," he said. "It's shocking to have a client sitting and waiting at a detention center, not able to call me."