I did find Virginia marriage records for two of her daughters and found that her middle initial was F. It possibly stood for Frances. A genealogy submitted to the FamilySearch website lists her parents as Abraham Beard and Mary King.
I do know that Elizabeth and Samuel moved to Johnson County, Missouri sometime between 1870 and 1880. At least two of their married daughters and their families moved along with them. By 1900, Elizabeth was widowed and living with her daughter. She died in 1901 and is buried next to her husband in the Kingsville Cemetery, Kingsville, Missouri.