They are not deporting the baby, but the baby is dependable/not an adult, so the baby goes where the one who had the custody goes does not matter their status. IF her father is legally in the US the baby can stay with the father does not mean that the mother has the right to do so.
She must read what the stamp says in her passport, the stamp must said that her visa is void and other stuff, possibly she is with the 3/10 year bar that depends how long she overstayed. If the overstay over a year after the expiration of her I-94 then is 10 years and does not matter if her bf is a USC he will have to apply for a waiver of extreme hardship before everything else. If her bf is a green card holder he cannot apply for fiance visa, and the waiting period is longer and anyway in both cases he will have to apply for a waiver if she has a ban to re-enter. The bar even applies for people with pending applications, so they should not exit the country until they have a result in their petitions.
The bar is over everything else.
The part that I don't understand is that she was in the US but she was caught in PR?