At present, there is no identified record evidence giving the specifics of Delilah's death and burial. All that can be mentioned with confidence is that her death occurred "before" 4 July 1844. We can infer that conclusion as derived from the date her surviving husband, Jeremiah, married his second wife.
Sources
"Indiana Marriages,1811-2007," database with images,FamilySearch(https://familysearch.org/pal:/MM9.1.1/KZC4-5KZ : 30 July 2017), Jeremiah Claxton and Delilah Pearce.01 December 1835; citing Orange County, Indiana, United States, various county clerk offices, Indiana: FHL microfilm 1,316,696.
"Indiana Marriages, 1811-2019," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:KZC4-5KZ : 8 April 2021), Jeremiah Claxton and Delilah Pearce, 30 Nov 1835; citing Orange, Indiana, United States, Marriage License, Indiana Commission on Public Records, Indianapolis; FHL microfilm 005014436.
"Indiana Marriages, 1811-2019," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:KZC4-LWV : 8 April 2021), Jeremiah Claxtan and Delilah Pearce, ; citing Orange, Indiana, United States, Marriage Registration, Indiana Commission on Public Records, Indianapolis; FHL microfilm 005014436.
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DNA Connections
It may be possible to confirm family relationships with Delilah 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 Delilah:
Peirce-649 and Pierce-346 appear to represent the same person because: My research only shows ONE daughter of Eleazar and Polly Pierce’s, named Delilah Matilda. My guess is that when Eleazar’s profile was merged, both Delilah’s were added.