Your relative may not have written the “Great American Novel” or otherwise noteworthy fiction, but it’s possible he or she wrote something else that was published.
Old newspapers may have contained a letter from your ancestor (either as a letter to the editor or as a “local correspondent). Trade publications may have contained a “how to” or career-based article written by your ancestor or about your ancestor. Publications of social or fraternal organizations may have also contained some of your ancestor’s writings.
Digital images of newspapers are available on a variety of online sites, both free and fee-based. Other publications may be available digitally at Google Books, Archive.org, or other archives of digital images of out-of-copyright publications.