You didn't include any dates, or approximate dates, in your query.So, I went looking to try and put them in a time frame.I did not find Hattie (maybe a nickname?), but did find the following on the TX Dth Idx Online 1964-1998:
Rayford James Hilburn, d 4 May 1988 Hunt Co, TX.
TX Births show a Dolly Jo Hilburn b 6 May 1934 in Camp Co, TX; mother Dolly Ellis; father Rayford James Hilburn.
Without dates not sure if the following is a match.Combined info from TX Dth Idx and SSDI:
Joseph Texas Hilburn, b 22 Feb 1905; d 20 Dec 1988 Tarrant Co, TX; last residence Arlington, Tarrant Co, TX; SS card issued in TX.[on SSDI he is listed as Joe T. Hilburn]
Forgive me if I make suggestions you've alredy tired, but have you looked at census records for the parents while they were still alive to see if your Hattie is listed in the family?
Maybe obits on the above Rayford or Joseph might have some helpful info. Happy Hunting.