She married twice. First to Henry Ferdinand Beam and second to Hezekiah Malone.
Sources
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"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M674-MQH : 12 April 2016), Elizabeth Gates in household of Joseph Gates, Harrison, Union, Arkansas, United States; citing family 614, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
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DNA Connections
It may be possible to confirm family relationships with Elizabeth by comparing test results with other carriers of her 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 Elizabeth: