His name is also sometimes spelled “Clayborne”, “Claiborne” or “Claibourn”. I am using the spelling from the marriage record of his son Dewitt. (That marriage record also lists the birth place of both of Dewitt’s parents as Elliott County, but Elliott County was not formed until 1869.)

1880 census of Elliott Co., Ky, Little Fork precinct, lists as household/family #15:
White, Clabron, 26, farmer, Ky Ky Ky; Susan, 22, wife, Ky Ky Ky; D. Wit C., 1, son, Ky Ky Ky. (The 15/15 grouping first lists the family of Elbert (22) & Mary E. (21) Sparks, with their 2-year-old son James, but it looks like this is just a failure to enter a new number for the White family rather than a shared household, since there is no relationship listed for “Clabron” to the Sparks, and when two unrelated families share a house they are generally given their own family number.)