My impression is that when a college football head coach is fired by a university, that coach is usually considered to be "persona non grata" at the university. I know that there are some exceptions, such as all of the recent Ohio State coaches who, despite being fired, still return to campus on occasion for official events.
I can't imagine a scenario in which either Bob Davie or Ty Willingham would ever be invited back to Notre Dame for any reason at all. While Weis would definitely be allowed to come back for alumni events, I can't see him being welcomed back for anything related to football.
But why are things different with Gerry Faust? When I went back to campus for a game in 2004, I remember Faust having a table outside of the bookstore in which he signed copies of his autobiography. He also participated in that panel discussion with Lou and Ara a few years back (the one that was moderated by Regis Philbin).
There's no question that Faust failed miserably as a coach at ND, and that the University fired him. So why is it that he continues to have ties to ND?