There are no Abernathy daughters on ancestry.com's 1930 Federal Census for the Texas county where Cross Plains is found, but there are 4 listed in the county where Rising Star is located, 1 in the county to the south of Cross Plains and 7 to the county south of Rising Star. None are listed as "Jute" and some are listed as black or colored so you may wish to examine all four counties on the 1930 Texas census: Callahan, Eastland, Coleman, & Brown. I also found no records at all for a "Jute Abernathy" on ancestry, so presume that 'Jute' was probably a nickname. Might I also suggest a search under a different surname variation? Or perhaps in the neighboring states?