Directories of heads of households have been published for major cities in Michigan. For example, the Family History Library has the following:
1856-1935 on 72 Family History Library films; 46 microfiche
Detroit directories from 1887 through 1915 may list the name and death date of individuals who died during the preceding year.
1856-1936on 36 Family History Library films; 4 microfiche
The best collection of directories is at the Library of Michigan. A description of their availability and use is in the Summer 1975 issue of Family Trails (see the "Periodicals" page.