A free woman could not give birth to a slave child. According to some jurists, however, a slave woman, however, could have a freeborn child. She only had to have free status sometime during her pregnancy. According to law, it didn’t matter if she had been enslaved or re-enslaved after the conception. The child of a woman who should have been freed but wasn’t** was also free.
Of course, this didn’t play out as simply in practice. How was a woman to enforce her child’s free status if she was a slave at the time of the child’s birth? Even a freedwoman might have some trouble if, as in the case of Petronia Justa, a freedwoman left her child in the care of her patron until she could raise it herself. In cases where the grant of freedom was in default, who knew when the woman or her child might actually obtain free status. This is not to say that none did, merely that it would have been difficult.
The Augustan marriage laws granted freedom from guardianship to freedwomen with four children. It is likely, however, that only her free children counted towards this total. Add to this the fact that slave women were generally not manumitted until they were in their 30s at the earliest, well into their childbearing years. As a result, the status of her children could have mattered to a freedwoman not only because of her own personal interest in them, but because it also had the power to affect her own as well.
*Marriage in Rome was limited to free (freeborn or freed) Roman citizens, with a few restrictions on who could marry whom and when. A senator or the child or grandchild of a senator, for example, could not marry a freedperson or someone associated with an unsavory occupation like acting, prostitution, or tavernkeeping.
**If, for example, someone’s will gave her freedom, but their heirs ignored this or for some other reason didn’t manumit her.
Paul, Opinions 2.24.1-9 - Diotima
The Julian Marriage Laws - Diotima
Pomeroy, Sarah. Goddesses, Whores, Wives, and Slaves: Women in Classical Antiquity. New York: Pantheon Books, 19.