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The options parents facing deportation have after they've been separated from their kids

(CNN) A new government document obtained by CNN offers parents separated from their children by US immigration authorities the option to be deported with or without their kids.

The document itself makes clear that the binary choice is only supposed to be for parents who have already been ordered deported from the country. But advocacy groups are raising concern that the document could be easily misunderstood or may be being presented to some parents detained under the zero tolerance policy before all their options to stay have been exhausted.

CNN reported last week that parents were being offered the option to sign voluntary departure orders to speed up their cases even if they still had other options -- and told they'll be reunited with their kids before they are deported if they do.

The form obtained Tuesday is the first document outlying the options for a parent facing deportation that has been made available to CNN.

The "Separated Parent's Removal Form" gives detained parents two options: Be deported with their child, or go back to their country of origin alone, so that the child can "pursue available claims of relief" in the United States without them.

The form was provided to CNN by the Southern Poverty Law Center and was verified by an ICE spokeswoman.

The Southern Poverty Law Center, a legal advocacy organization focused on civil rights, says it was first made aware of the document on Friday and say it has been presented to "a few of their clients" currently in detention.

"This form is for detained alien parents with administratively final orders of removal" the document's first line reads.

"Any such decision must be made affirmatively, knowingly, and voluntarily," it says, adding, "This form must be read to the alien parent in a language that he/she understands."

SPLC alleges that it has clients who were offered the form despite not having final orders of removal, but declined to provide individual names and case numbers that could have been verified.

ICE spokeswoman Jennifer D. Elzea said it is "long-standing policy" to offer parents facing deportation the option of leaving their kid behind, noting it is "not uncommon" for parents to elect to do so, historically. Any child who remains in the United States in the custody of the government or with a family member is allowed to pursue their own right to stay, and ICE "does not interfere" in that decision, Elzea said.

As for the specific form, ICE could not immediately answer what training is provided to agents using it in the field, but noted its intent.

"As is stated on the very top of the form, this form only applies to parents with a final order and who are part of a specific class action suit," Elzea said. "This form has absolutely nothing to do with those who have pending asylum claims."

"An individual who has received a final order of removal has already been given the opportunity to make a claim of fear about returning to his or her country of citizenship," she added.

The confusion over the form is indicative of the broader concerns immigration attorneys have about how much detained parents separated from their children can understand about their situation. Many of them are Central American and may not speak either English or Spanish, rather speaking indigenous languages. Parents have also described the distress of not knowing where their children are, and attorneys who represent them describe some cases where there is perceived pressure to agree to deportation in order to be reunified.

SPLC immigration attorney Gracie Willis said her organization has two cases where they believe individuals who did not have final orders of removal "have been pressured to sign this document." CNN was unable to verify those claims without the names of those individuals.

Willis did not allege that ICE was acting in bad faith, but called the document and its potential use beyond final deportation orders "concerning."

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