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Dear Ms. MacPhail,
Thank you for posting your request on History Hub!
We also searched the Population Schedules for the 1850 Census, Population Schedules for the 1860 Census, Population Schedules for the 1870 Census, Population Schedules for the 1880 Census, Population Schedules for the 1900 Census and Population Schedules for the 1930 Census in the National Archives Catalog but were unable to locate any Fails from (or nearby) Goldsboro, NC as digital images have not yet been added to the catalog.
Therefore, we searched Ancestry. In the census records for Fails living in or near Goldsboro, Wayne, NC, we located three households with the surname Fail: (1) a William and Louisa in the 1850, 1860, 1870 and 1880 census records, as well as Louisa living with her son, William R. Fail, and family in the 1900 census; (2) a Lewis and Liecey Phail in the 1850 and 1860 census; (3) a Needham and Phoebe (Pharibee) Fail in the 1860, 1880 and in the 1900 Needham is not listed but Phoebe and some of their children are.
We also located a 1950 city directory record for a William R. Fail, son of William and Louisa. You may want to check city directories to help narrow your search. And there is a Needham W. and a Mary Phail on the 1930 census. This Needham may be the son of Needham and Phoebe Fail.
To view these records on Ancestry, there may be a fee. Or you may view the records online at one NARA's facilities for free via ALIC. For the nearest NARA location, please consult our web page at https://www.archives.gov/locations/. Many of the records are also available on FamilySearch for free.
For immigration records, we suggest that you search the State Library of North Carolina’s Naturalization and Citizenship records.
We hope this is helpful. Best of luck with your family research!