Professor M wrote in the Vincent thread about Michael
he can't retire: they keep pulling him back in.
What do you think did Michael do after he lost his daughter? We'll never really know. All we have to conclude what's happened are the flashback scenes (the dances with Appollonia, Kay and Mary) and the last scene in Sicily.
I believe that (maybe after a short return to New York and some psychological treatment after the nervous breakdown) he stayed in Sicily in Don Tomassino's house. He died alone. In the book Vito's last word's are "Life is beautiful." If Michael had some last words they probably would have been: "Life is unfair."