NEVER waste your money obtaining copies of death certificates when you are not sure the person is even correct.A little bit of research identified the one dying in Lane County was not the correct person.The correct person was found in Missouri. Often it is much more fruitful looking for the correct persons that looking at wrong ones.When you post, post information about the person, their date-of-birth is especially helpful, place of birth, parents, siblings also help identify the person from another.
The 1930 Census for Springfield, Lane County, OR
Jennie Barnard, age 78, born in New York to father born in NY, mother in Ohio.She was listed as a widow.She was living as a boarder in the home of Oswald Olson, age 36, born in Wisconsin; and his mother Emma C, 62, born in Sweden, Widow.
The 1920 Census for Springfield, Lane County, OR
Fred Barnard, 65, born in NY
Jennie, wife, 67, born in NY.
So, it appears very unlikely this is the same couple based on locations of birth.
From another of your postings:
"Fred Barnard b. 1872 in Missouri, son of James J. & Eliza McAdams Barnard, married Jennie Billings in 1893. I found them in the 1900/1910 census Missouri but can't find them later."
The 1910 Census for Asbury, Jasper Co, Missouri.
Fred Barnard, age 36(1873/1874), in Missouri to father born in Indiana, mother in Missouri, cigar maker/factory, renting.Married 17 years (1892/1893).
Jennie, age 36, born in Illinois to both parents born in Indiana, Operates(operator?) Telephone/SB.Mother of 2/2 living
Eunice, 15(1894/1895), born in Missouri
Freda, 6(1903/1904), born in MO
Nancy Billings, Mother-in-Law, 78, widow, born in Indiana to both parents born in Virginia.Mother of 4/2 living.
The 1920 Census for Joplin, Jasper County, Missouri
John W. Seibel, age 42, married, born in Ohio to father born in Germany, mother in Ohio, Machinist/Machine Shop.
Jennie, age 40, born in Illinois to both parents born in Indiana
Eunice B, age 25, born in Missouri
Freda B, 16, born in Missouri
So it appears for whatever reason, Jennie remarried.