Status under Roman law passes through the female line unless the specific marriage form of conubium ensures succession through the male. After allk, Roman law stipulates unequivocally that the father can never be known with certainty, but the mother always. The child of a slave woman is a slave of her owner by birth (IIRC it's Juvenal who makes a joke about a slave owner all of whose slaves look suspiciously like him...)
As to what would happen - that depended awfully on the circumstances. There was no particular shame to impregnating the occasional slave girl. slave women themselves, of course, had no way of refusing and thus it was not considered that this reflected on their honour (inasmuch as that concept applied to slaves at all). Selling a pregnant woman would, from a Roman POV, be a pointless waste of valuable resources. Houseborn slaves commanded a premium. Since, s.a., pater semper incertus, a slave owner might simply assume the new child into his household as a slave, offspring of who knows, really. IN larger households, that's the most likely outcome.
A small household with just one or two slaves might not have the resources to raise a child and the master choose to expose it after birth. That, too, was commonplace. Babies would normally be placed on communal dungheaps or other public places and collected by whoever wanted one to raise as hios own, or as a slave.
In some cases, where the slave is the permanent companion of her owner, the child might be raised as his and freed on attaining majority. With those kinds of relationship, though, it was customary to free the mother well before she got pregnant. Having a freedwoman concuibine as a long-term life partner was quite common. Her children,. being born free and (assuming the person doing the freeing was a Roman citizen), to citizen status could even be adopted by the father.