You might want to look next door in Hamilton County for parents of Elizabeth. John Anderson bio might lead you to find her parents:http://www.carolyar.com/Illinois/Bios/Anderson.htm
Neither of the Hails bios I could find mention the man who Elizabeth Anderson married:
Thomas Hails was born in 1794, in North Carolina. Sarah E. Justice was born in Virginia on December 22, 1798. During the War of 1812, Thomas Hails fought in the Battle of New Orleans with General Jackson. Previous to their marriage Thomas Hails and Sarah Justice Hails moved to Tennessee. One of their 11 children, Marcus Hails, was born in 1826.
Thomas, Sarah and family were among the early families to move to Jefferson County, ILL.. in 1827. They settled in Section 10 and 11 of Shiloh Township, made farming their way of life and lived there until their death. Both were buried nearby in Old Shiloh Cemetery: Thomas on Oct. 25, 1857 and Sarah on Feb. 10, 1871.
Source: Facts and Folks of Jefferson Co, IL - 1978 - Jefferson County Historical Society
JOHN W. HAILS, farmer, P.O. Richview, was born in Sumner County, Tenn., March 19, 1823. His parents were Thomas and Sarah (Justice) Hails, his father a native of North Carolina nad his mother of Virginia. Previous to their marriage, they had moved to Tennessee and in 1827 came to Illinois, settling in Jefferson County, near Mount Vernon, where they lived until their death. His occupation was that of farming making his home on the wild prairie, with Indians camping near. They were the parents of eleven children, six of whom are still living. He was in the war of 1812, and fought with Gen. Jackson at New orleans. Both were members of the Methodist Episcopal Church and had been since early life. The subject of this sketch was reared on the farm and educated in the log schoolhouses of the day. When he reached his majority, he began life as a farmer and has followed the same occupation to the present time, being engaged in stock-raising in connection with his farm. When he left the old home, he came to his present farm and began to improve it. He has now a well-cultivated farm of 330 acres, and besides this has deeded to this children 360 acres. In politics, he still holds to the opinions of his fathers. Has held various township offices, and is now filling the osition of Highway Commissioner. He and his wife are both members of the Methodist Episcopal Church (South). He was married August 8, 1848 to Annis M. Casey, daughter of F.S. and grand-daughter of Abram Casey. Mr. and Mrs. Hails have one child, dead and eleven living -- Narcissus C. (deceased), Thomas F., Alfred M., Zadok C., Sarah Harriet J., Ellen, Ida P., Mary, Charles, John and Samuel T. -- all living in the immediate neighborhood.
Source: History of Jefferson County, IL - 1883 - by William Henry Perrin