Jesse Moody died in Greenville, South Carolina, probably in early 1788. His widow Dinah Moody applied for letters of administration for his estate on 10 Feb 1788. (Greenville Co., SC. Probate Records Apartment 5 #338.) You can find the two documents from the file online at FamilySearch, Greenville Probate records 1787-1868 Files 04-06, Nos. 215-420, Image 375 of 730. The first document in the file, appointing the estate appraisers, is dated incorrectly as 1780. The second record, appointing Dinah as administrator, is correctly dated as 1788.
I am sure the 1780 date is wrong because Jess and Dinah sold land in 1787:
Greenville Co. DB A:278. Feb 9 & 10, 1787. Jesse Moody, planter, to Joseph Meacham, planter, lease & release, 100a on Golden Grove Cr. waters of Saluda Riv, part of 400a granted 15 Oct 1784 to Benjamin Rice, above ancient boundary, S of James Seaborn & Nathaniel Pendleton's land. S/ Jesse (E) Moody & Dinah (X) Moody
Wit: Thomas West, Jos.(E) Richardson,Richard West,James West, Amos West.
Wit. oath 18 Aug 1788 by J. West.
The widow Dinah Moodey was on the 1790 census in Greenville.
It doesn't appear that Jesse Moody of Greenville had a second wife.