I am reporting a follow-up on this thread. I had NEHGS do research on this couple with their Boston resources. This is a short report of their findings.
Henry Adams died of "intemperance" on November 9, 1833, at age 40. He was buried in the South Burying Ground, which was later filled in and developed. Henry had bought land in Boston in 1819, but sold it for less than what it was worth in 1830. The picture suggests his business as a truckman was failing.
The NEHGS genealogist did not find any death records for Celia Eliza Buck Adams. However, my best guess is that she returned to live in Killingly, CT with minor children. There is no record of a later re-marriage or of her death. One of her daughters married an Adams cousin, and continued to live in Killingly. This couple, Frederick A. Adams and Elizabeth Hannah Adams were married in 1850, and left children. Their daughter Julia A. Adams (1851-1907) married Eugene Peck in Killingly, and had two daughters. Their son Edward N. Adams (1853-1898) was apparently unmarried.
If any descendants are interested, I will share further information.