In 1867, she married Joseph Hancock, who was likely her first cousin. They had two children:
Mary A (Mamie) (1869-1946)
George W (1870-<1950)
She died on 19 Apr 1871 in Elizabeth, Illinois.
Sources
Julia Hancock (FamilySearch) (contains links to other sources).
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DNA Connections
It may be possible to confirm family relationships with Julia by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Julia: