I agree there were probably two different Frederick Close persons who lived in Michigan about the same time and that the Bay City family is not the one I am researching.I do know that "my" Frederick Close married Mary Kline on 18 April 1872 in East Raisinville, Monroe County, Michigan.Mary was from Sandusky/Seneca Counties in Ohio, along with her sister Sarah.They were daughters of Lewis Kline and Susannah Powell.
I found Fred "Kloos" born February 1851 in NY living in Dundee, Monroe County, Michigan in 1900, with wife Mary born July 1849 in Ohio and daughter Emma J. born October 1881 in Michigan.In 1910 they were in Bedford, Monroe County, listed as Fred and Mary "Close," with 28-year-old daughter Jennie (who was probably the "Emma" in 1900, or "Emma Jane.")They had two other known daughters -- Margaret A. "Kloose" born 26 Nov 1873 in LaSalle, and Susan M. "Kloos" born in Ida.All Monroe County.
By 1920 Mary "Kloos" was a widow, living alone in Milan, Monroe County, Michigan.It would appear that Fred died between 1910 and 1920.