I cannot tell you exactly when Fountain and Sarah died, but I can give you a general idea.
Fountain Hasty - The notice was published in The Citizen (Berea, KY) on 12 November 1903. The date of the incident, however, was on 4 November 1903. It happened in Danville, Boyle Co. KY.
The end of the notice says "Hasty will die." It does not say he is already dead. So I would assume that to mean that Fountain was still alive at the time the newspaper went to press. It's a good bet he died in November 1903.. unfortunately, there is probably not a death certificate for him to obtain an actual date.
I have a copy of the newspaper article, if you need it.
Sarah Scarborough Hasty - She died in Stringtown, Mercer Co. KY in 1916. Kentucky Deaths and Burials, 1843-1970, gives this information along with her father's name.. Johnson Scarborough.. Mother Unknown.
She is listed as Sally Ann Hasty in the record, and there is a listing for her in the Kentucky Death Index. It shows her date of death as 1 May 1916, and her Death Certificate Number as 13762.
If this is indeed the wife of Fountain Hasty, then you now know when and where she died. The death certificate will probably list where she was buried.. hopefully in the same place that Fountain is buried. It is not currently online, so it will need to be pulled from Kentucky Archives.