If a white woman had a black baby what would happen to the baby back in slavery time?

There is not a excact answer, it's the family's desicion, but if the white woman wants the child, she can keep it, but if she doesn't or can't, she'd have to give it away for someone to adopt, which likely will be a black, or just leave it somewhere for someone to find. Or maybe, this is very mean, but I've read that some even kill them. Unbelievable! Who would kill their very own baby that she, and no one else in the universe had that's her very own, and not love it?