There was a student named Catherine DeRosset at the Mordecai school, enrolled for two sessions, in 1811; Dr. A. J. DeRosset was the adult on her account. As it happens, Catherine DeRosset was from a prominent Wilmington family, and became a friend to Rachel Mordecai after the school years. Rachel Mordecai even named one of her daughters partly for Catherine (her daughter Mary Catherine Lazarus, born 1828; naming story from a letter, from Mary Orme to Ellen Mordecai, 26 September 1828, Mordecai Family Papers, SHC). So we know a good deal about her family and how her life turned out.
(Note: For a very long time, I remember that she was listed as Catherine Prosser in my draft versions of the school rolls, even while the name DeRosset was familiar in other Mordecai-related contexts. So there's a reminder that handwriting can be a major cause of error.)
Armand John DeRosset (1767-1859) was a doctor of Huguenot ancestry, like his father and grandfather before him. Catherine Gabrielle DeRosset was the eldest child of her father's second marriage, to Catherine Fullerton (1773-1737). Catherine had three younger sisters, and a younger brother Armand Jr., as well as an older half-brother (who was also her cousin--their mothers were sisters), named Moses. Catherine was ten years old when she went to the Mordecai school (turned 11 there). She may well have attended school with cousins; her paternal aunt was Mrs. Henry Toomer, her maternal grandmother's maiden name was Toomer, and there was a Sarah Toomer at the school during the same sessions as Catherine was there.
Catherine married a Methodist pastor, Rev. William Magee Kennedy (1783-1840) in 1835, becoming stepmother to his children; they moved to Columbia, South Carolina. Catherine was forty the year she was widowed, after just five years wed; she and her ten-year-old stepdaughter Cattie moved back to Wilmington at that juncture. Catherine and Cattie were close; here's one of Cattie's letters to Catherine, from during the Civil War. (Many years later, Cattie would marry Catherine's younger brother, Armand Jr.) In Wilmington as a youngish widow, Catherine was a co-founder and first president of the Ladies' Benevolent Society, and founder of a home for elderly women, opened as Old Ladies' Rest. She also worked briefly as a nurse at a wartime hospital in Petersburg, Virginia, in 1861 (letter, Cate Kennedy to her sister Liz, 1 November 1861, DeRosset Family Papers, SHC).
Catherine DeRosset Kennedy died on Christmas Eve, 1889, age 89. Old Ladies' Rest was renamed the Catherine Kennedy Home in her memory, and retained that name until it closed in 2000, considered at the time the oldest "home for the aged" in the US. The Catherine Kennedy Home Foundation remains a granting entity, supporting causes that help senior citizens.
(Image: State historical marker for the Catherine Kennedy Home in Wilmington. Reads: "Catherine Kennedy Home / For the elderly. Grew from Ladies Benevolent Society. founded 1845. First home, 1879, stood four blocks east.")
One website calls Catherine DeRosset Kennedy a "driving force"; compared to most of her Mordecai classmates, she certainly took a more public role in pursuing her interests. She's even the subject of a recent master's thesis, "Catherine Kennedy DeRosset's Independence: A Modern Historian's Analysis of a Nineteenth-Century Southern Woman" (MA, Georgia State University 2003) by Angela H. Gilleland.