I cannot find death or cemetery records for James or Annie. But the fact that their daughter Annie is buried in the same cemetery in Lynchburg as Dr. John Christian Mundy, his wife Cynthia, and their sons Dillard and Stephen is good evidence that the James A. Mundy who married Annie is the same one who was the son of Dr. John C. Mundy and Cynthia Dillard.

1900 census of Nelson Co., Virginia, Lovingston ward 1, enumerated 22 June, lists on p. 16B as family #305:
Munday, James A., 41, b. Aug 1858, railroad contractor; Anna C., wife, 35, b. Jan 1865, married 13 years, mother of 1 child, 1 living; Anna May, dau, 9, b. Sep 1890. Afee, George, hired man, 65, b. 1835, widowed, white, manager of farm. Ferell, Mary, servant, 17, b. 1882, single, black, cook. Wood, Magie, servant, 13, b. 1887, black, house maid. All born Va Va Va.

1910 census of Nelson Co., Virginia, Lovingston district, enumerated 14 May, lists on p. 17B as family #338:
Mundy, James A. Jr., 51, general construction work; Annie C., wife, 44, first marriage for both, married 23 years, mother of 1 child, 0 living. Furgusen, Franky, cook, black, 23, single. All born Va Va Va.

The “Jr” is apparently to distinguish James from his uncle of the same name.