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James Parchman (57) and wife Sarah (50) can be found in the 1850 census of Harrison County, Texas. She is listed as "J", but all the dates check out for it to be Sarsh. Nine children are there with them, W. 25, W. (Whitfield)21, William 19, J. M. (James Madison) 16, M. V. B. (Martin Van Buren) 14, J. (Nancy Jane) 12, S. (Sarah Ann) 10, L. M. (Lemuel) 7, M. P. (Mary Permila) 4. Eldest sone Liles was in Missisippi in Monroe Co., Daughter Elizabeth White was in Mississippi, daughter Martha was married to John Secrest and in 1857 living in Texas. I don't know her whereabouts in 1850, but I doubt that it was Lawrence County. In 1857 she is listed as living in Gonzales Co. Tx. All of the children that came to Texas with James (ca 1847) stayed in Texas and the ones that did not can be found in Mississippi.
James died in Gonzales County, Texas in 1857. A court action to settle his estate names all of his children. Elizabeth Smith was deceased by this time as her children are named as heirs. As part of the action the chilren were requesting a guardian to be appointed for James' three youngest children. Sarah is not memtioned, so it's probably safe to assume that she died between 1850 and 1857, although whether in Harrison Co. Tx or Gonzales Co. Texas is not certain.
James can also be found in the 1830 census in Fayette County TN, near his brother Jesse who also moved to Texas. From all the evidence, it appears that James and his chilren moved to Monroe Co. MS, between 1820 and 1830. Son Liles and daughter Elizabeth stayed there. James went back to TN for a while and then he and the rest of the family moved to Texas.