I believe that would be Isaac J Rigsby born 1895 NC to John Vernon Rigsby born 1848-02-08 Orange Co NC died 1912-07-22 + Mary Leigh born about 1860 NC. He is the only Isaac I know of in Durham Co in that time period.
John's parents were Jesse O II Rigsbee born 1808-06-22 died 1881-02-01 Durham NC + Mary Vickers born 1810-01-09 died 1889-07-23.
Jesse's parents were Jesse O Rigsby born 1764 died 1827 + Elizabeth Pickett born about 1780 Orange Co NC died 1850-04-19.
I haven't found the older Jesse's parents, but he is probably from one of the NC Rigsby families. There were several Jesses there in the mid-1700s, and this one is no doubt related to them somehow.
I don't have much information on the Rigsbys past 1900 or so, so I'm afraid I can't help you with Isaac's living relatives. I do know he had a brother Albert born about 1878, and sisters Arlina, Elizabeth, and another whose name I haven't found.