Here's a list of coaches that got fired within a few years after winning the COY: 1963-1964 – Alex Hannum, San Francisco Warriors: fired! (1966) 1965-1966 – Dolph Schayes, Philadelphia 76ers: fired! (1966) 1972-1973 – Tom Heinsohn, Boston Celtics: fired! (1978) 1973-1974 – Ray Scott , Detroit Pistons: fired! (1976) 1974-1975 – Phil Johnson, Kansas City-Omaha Kings: fired! (1977) 1975-1976 – Bill Fitch, Cleveland Cavaliers: fired! (1979) 1977-1978 – Hubie Brown, Atlanta Hawks: fired! (1981) 1979-1980 – Bill Fitch, Boston Celtics: fired! (1983) 1980-1981 – Jack McKinney, Indiana Pacers: fired! (1984) 1981-1982 – Gene Shue, Washington Bullets: fired! (1986) 1986-1987 – Mike Schuler, Portland Trail Blazers: fired! (1989) 1987-1988 – Doug Moe, Denver Nuggets: fired! (1990) 1990-1991 – Don Chaney, Houston Rockets: fired! (1992) 1991-1992 – Don Nelson, Golden State Warriors: fired! (1995) 1994-1995 – Del Harris, Los Angeles Lakers: fired! (1999) 1998-1999 – Mike Dunleavy, Portland Trail Blazers: fired! (2001) 1999-2000 – Doc Rivers, Orlando Magic: fired! (2003) 2001-2002 – Rick Carlisle, Detroit Pistons: fired! (2003) 2005-2006 – Avery Johnson, Dallas Mavericks: fired! (2008) 2006-2007 – Sam Mitchell, Toronto Raptors: fired! (2008) 2007-2008 – Byron Scott, New Orleans Hornets: fired! (2009) 2008-2009 – Mike Brown, Cleveland Cavaliers: fired! (2010) Reference: http://www.sportsgrid.com/nba/how-often-do-nba-coaches-of-the-year-get-fired/
The second half of that list, Stotts included, are mostly coaches that don't do their job particularly well.
Pop can be named as a COTY every year because of the team record, but he can not be fired after the reward either because he is a GM, so he does not care if he is named for COTY or not, the reward should be given to others.
Popovich obviously will never be fired by the Spurs, but he'll probably step down the moment Duncan retires. I don't see him wanting to preside over a rebuilding effort at his age.