We asked our SW about what would happen if a birthmom died in childbirth, and she's going to have to research the answer. They must have never had it happen. She did say that the birthmom signs relinquishment paperwork after the birth (whether that's 5 minutes or 2 hours or more afterward), so obviously this situation could be an issue. She said she would assume that they may have to deal with county child services.
I'll keep you posted.