From Census records, I've seen an assortment of situations. One was a teen mother at home with her parents and siblings. The baby's father lived next door and was about 10 years older. They married after the child arrived, but not immediately. They had many more children and lived out their lives together. This is one of the few "happy endings" I've found. Often, the young mother lived with her own mother, and the child was reported as a sibling or cousin. Another baffling household had the young mother living with her parents and sibs, the child correctly attributed to the mother, and with the father's surname. That father never married, and he supported the child. The mother, though, changed her name and identity several times, even while living with her own parents. Twice, in researching cemeteries, I've found an infant's grave set far from the rest of the family, with the baby's mother missing from the family plot. In both cases, I traced the mother to a life of missionary work in the same denomination of church, and both spent time in China. This suggests a load of guilt and/or shame the mothers were trying to undo with their mission which, for both, began immediately after the babies died.