Hi Charles - It seems Abel did make it through the war alive. And I see about 5 Baggetts in the Texas Confederate muster cards.
Here is a genealogical bio - maybe you can find clues. other than what George listed.

-When Abel Green Baggett was born in 1827 in Franklin County, Tennessee, his father, Joseph, was 42 and his mother, Jestin, was 26. He married Nancy Beckum and they had six children together. He then married Susan and they had one son together. He died in 1885 in Williamson County, Texas, at the age of 58.
-Abel Green's brother Abraham C was born in 1829 in Franklin County, Tennessee when Abel Green was 2 years old.
-Abel Green's sister Mahala Isabella was born on April 20, 1832, in Franklin County, Tennessee when Abel Green was 5 years old.
-Abel Green's father Joseph Blakely passed away in 1840 in Franklin County, Tennessee, at the age of 55.
-Abel Green's brother Thomas H was born in 1840 in Franklin County, Tennessee when Abel Green was 13 years old.
-Abel Green's mother Jestin passed away in November 1846 in Franklin County, Tennessee, at the age of 45.
-Abel Green Baggett married Nancy Beckum on January 19, 1847, in Franklin County, Tennessee, when he was 20 years old.
-His daughter Mary E was born in 1848 in Franklin County, Tennessee.
-His daughter Malissa Isabel was born on June 12, 1851, in Franklin County, Tennessee.
-His son William Jackson was born in December 1851 in Franklin County, Tennessee.
-His daughter Missouri was born in 1853 in Franklin County, Tennessee
-His son George Calloway was born on August 24, 1854, in Franklin County, Tennessee.
-His son James M was born in 1858 in Franklin County, Tennessee.
-Abel Green Baggett lived in Franklin County, Tennessee, in 1860.
-ENLISTED, July 1861: Private; Bernard Timmons, Captain, Bachelor Rifles, Inf., Fayette, Cty., TST, Remarks: R&F 44; Hdqrs. LaGrange; Co
-POSSIBLE enlistment, not sure: A. Bagette, Private, Capt. W. W. Parks, Reserve Company, Ellis County, Beat No 6, 19th Brigade TM enlisted August 1861
-His wife Nancy passed away in 1862 in Franklin County, Tennessee, at the age of 42. They had been married 15 years.
-Abel Green's brother Abraham C died on May 12, 1864, in Moultrie County, Illinois when Abel Green was 37 years old.
-Abel Green Baggett married Susan in 1864 in Tennessee, when he was 37 years old.
-Abel Green's brother Thomas H died about 1864, in Warwickshire when Abel Green was 37 years old
-His son Thomas was born in 1865 in Franklin County, Tennessee
-Abel Green Baggett lived in Franklin County, Tennessee, on August 1, 1870.
-Abel Green's sister Mahala Isabella died on July 11, 1877, in Travis County, Texas when Abel Green was 50 years old.
-His son William Jackson passed away on December 18, 1878, in Williamson County, Texas, at the age of 27.
-Abel Green Baggett lived in Williamson County, Texas, in 1880; He is a farmer; 2nd wife Susan is a housekeeper, and daughter Mary lives with them. Dwelling 251; Precint 6
-Abel Green's brother William Moses Andrew died on June 5, 1883, in Moultrie County, Illinois when Abel Green was 56 years old.
-Abel Green Baggett died abt 1885 in Williamson County, Texas, when he was 58 years old.

-His family is located in Austin, Tx in the 1910 census
-Second wife, Susan died 1914 of a stroke. Her death certificate in on findagrave.com maintained by a “Don Weaver”. An “A. G. Baggett, signed the death certificate. Might be a jr?
She is buried in Masonic Cemetery
-note on Nancey (1st wife) Note by Don Weaver:
Nancy Beckum "Baggett" was listed as wife of Green Baggett in the 1860 Franklin County, Tennessee U.S. Census. She died shortly after the census was taken. She marred Abel G. (Abel Green) Baggett in 1847 in Franklin County, TN. In 1870 Green "Baggette" is listed with his new wife, Susan, and Nancy's children, living in Franklin County. The date and place of Nancy's death is unknown.

More information: In the 1870 census, James M. "Baggette", is listed in the family census. His age is given as 12 years old. James "Baggett" is listed in the 1880 census, living alone, in Franklin County, as 20 years old - making him born in 1860. Nancy may have died in child birth giving birth to James. Not varified. In the 1880 Census, A.G. (Abel Green) Baggett, and other family members, are listed in Williamson County, Texas. James and other family members stayed behind in Tennessee

Note: It appears Don Weaver knows quite a bit about the family. Do you know him?

Note: there is a “Project preservation Winchester TN File #1870-647” attached to Abel Green Baggett. If you want more I can send to you.

I also do not have a verified death date or cemetery. It may have been after 1885
I found Abel G Baggett; Dallas City Directory 1888; Southwest Corner Howell Peak