|Delaware Public Archives. https://archives.delaware.gov/100/wearelivingandlearning/Taking_Responsibility.shtml|
Communities have always felt the need to ensure that they are not stuck with paying the bill for those living in poverty. In an earlier time, a woman with a child but no husband might be at risk for living in poverty.
And so we have bastardy bonds.
I probably don't need to explain what the term "bastard" means. But you may be wondering what a bastardy bond was. "Bastardy bonds were typically posted by putative fathers of illegitimate children to insure that the child was supported without public expense."*
"Bonds and records typically give the name of the father, his bondsman, as well as that of the mother and child, and the amount of the bond posted. Bastardy records may also include presentments against and examination of unwed mothers and mothers-to-be, warrants to bring putative fathers to court, and receipts for payments made on behalf of bastard children."*
So a female ancestor who had a child out of wedlock might be documented in a bastardy bond. These are great records for placing her in a time and location as well as confirming her as the mother of a child and possibly linking the father to them.
Look for these records through the FamilySearch Catalog, local courthouse or state archive. You might also want to read up on the existence of bastardy bonds in the location your ancestor lived.
The Legal Genealogist - Looking for Bonds
Delaware Public Archives - Taking Responsibility
FamilySearch - Catalog - Bastardy bonds and records (North Carolina), 1736-1957
FamilySearch - Catalog- Bastardy Bonds, 1880-1911 (Georgia)
*Bastardy Bonds and Records 1735-1966. State Archives of North Carolina.