I was at the Burton Historical Collection and searched the Detroit city death index microfiche and found that William Gearhart died on June 20, 1928 at the age of 33. The death certificate number is 08620.
I also checked the available city directories and found the following information:
r = residence
h = home
cond = coductor
prsfdr = press feeder
agt = agent
clk = clerk
1919-1920 Gearhart, Wm L, cond, r1084 Medbury Ave.
1920-1921 Gearhart, Anna, bindery girl, h6683 Wales
Gearhart, Wm L, cond, h6685 Wales
1922-1923 Gearhart, Wm L, cond, h6685 Wales
1923-1924 Gearhart, Anna, prsfdr, r6685 Wales
1923-1924 Gearhart, Wm L, cond, r6685 Wales
1925-1926 Gearhardt, Wm L, cond, r6685 Field Ave (st name change?)
1926-1927 Gearhardt, Wm L, cond, r6685 Field Ave
1927-1928 Gearhart, Wm L (Anna), cond, DSR h6685 Field Ave
1928-1929 No entry for Gearhart, Gearhardt, Gerhardt, or Gerhard
1929-1930 Gearhardt, Anthony (Anna) agt, r2809 Lawton Ave
Gearhardt, Anna, student, r2809 Lawton Ave
1930-1931 Gearhart, Anna (widow Wm), clk, r8017 Townsend Ave
1932-1933 Gearhart, Anna (Widow Wm), r8017 Townsend Ave
1934 Gearhart, Anna (Widow Wm), r8017 Townsend Ave
1935 Gearhart, Anna (Widow Wm), printer GM & TC co, r8017
1937 Gearhart, Anna (Widow Wm), r8017 Townsend Ave
1940 Gearhart, Anna (Widow Wm), r8017 Townsend Ave
1941 Gearhart, Anna (Widow Wm), r8017 Townsend Ave
So it looks like Anna and William did live together in various residences from 1919 through 1928. In 1929 I could find no listing for her at all under any spelling (and note in 1925-1926 the name was misspelled Gearhardt). I don't know what to make of the 1929-1930 listing showing a Gearhardt family of William and wife Anna with Anna, a student, living with them. Could these be family of William's who took Anna in? Perhaps she went to school?
Starting in 1930-1931 and up through 1941, she shows up at her parent's home on Townsend, sometimes with her work employment listed. I did not find Anna in the directories available after 1941. But I also did not find her in the death index under the name of Anna Gearhart. She might have remarried or moved out of the city and would not be listed in the death indexes, which only go through the 1960s (I think).
I did not check the directories for her family's name. Perhaps I will do that next trip to Burton and see if she turns up after 1941 in the same house with a different name.
Hope this helps!