I wonder if "Katie M." Fernald from the 1870 census was perhaps listed as "Hattie M.",in the Norfolk county probate index. There is an adoption record and she resided in Boston in 1879. She would have been about 10 if it is her. If Samuel and or Elsie died, that might explain why I can't find them in 1880.
That's about all I can gather on this family without digging deeper. Both Lemuel and William S. Fernald (Sr. of Maine), did have other children. Probably in the Quincy and Boston area. And maybe Chelsea, since that's where the picture was from! I'm surprised there isn't much info on this branch of Fernald's.
Hopefully, some of this will connect somebody who has more clues or is looking!!
Katie if she was still living in 1880, may have been adopted. So perhaps she married and had children. Her sister Mary was adopted by her Uncle. Even though she was still single in 1900 at age 34, It's possible she married and had children by 1910. If not, that part of the branch sadly may have died out.
How did you come by the picture Kate? Are you related, or is it a coincidence you share the same name as Katie?