The House of Closed Doors (The House of Closed Doors #1)
Jane Steen

Nell's stepfather Hiram sends Nell to live at the Poor Farm of which he is a governor, to await the day when her baby can be discreetly adopted. Nell is ready to go along with Hiram's plans until an unused padded cell is opened and two small bodies fall out.
Nell is the only resident of the Poor Farm who is convinced that the unwed mother and her baby were murdered, and the incident prompts her to rethink her decision to abandon her own child to her fate. But the revelations to which her questions lead make her realize that even if she manages to escape the Poor Farm with her baby, she may have no safe place to run to.