Overstayed visa, leaving the USA with children without partner's approval [closed]

A good friend of mine is in an incredibly delicate situation. I hope someone here can help as I can't find anything relevant online. She has been living in the US for over 4 years. She, partner and kids have entered the US on a tourist visa and overstayed. She is breaking up with partner and wants to go back to her country of origin. Her partner is playing hardball and says he will not allow the kids to leave the country. I don't want to go into much detail here, but she has been in an abusive relationship.

The U.S. customs and border protection states the following:

Unless the child is accompanied by both parents, the child must have a notarized letter from the other parent or signed by both parents stating, "I acknowledge that my son/daughter is traveling outside the country with [the name of the adult] with my permission."

If worse come to worst, she can get in touch with immigration and they will probably deport everyone. I believe this would be a terrible outcome as it would be a trauma for her and kids.

So finally, here is my question: My friend is not a US citizen and has overstayed her visa in the USA. Can she buy tickets and leave the USA with her 2 kids? Will she be allowed to leave the USA with 2 kids without her husband's explicit approval?