Before coming to Detroit, Caldwell, 62, coached the Colts for three seasons, compiling a 26-22 record.

Fox was fired from his third N.F.L. team, although it was the first time he left with a losing record. The Bears were a troubled, losing team when Fox arrived in 2015, and he was charged with rebuilding the roster. He may have accomplished some of that — the Bears have a promising young quarterback in Mitch Trubisky — but the team played conservatively and appeared listless and overmatched.

The crowds at Bears’ home games this season grew more sparse with each defeat as the team finished last in the N.F.C. North with a 5-11 record. In three seasons, Fox, 62, had a 14-34 record.

Fox’s overall head coaching record is 133-123. In nine years with the Carolina Panthers, he made the playoffs three times and took the 2003 Panthers to the Super Bowl, where they lost by three points to the New England Patriots.

In 2011, Fox took over the Denver Broncos and led the team to four successive postseason appearances. The Broncos were routed 43-8 by the Seattle Seahawks in the Super Bowl after the 2013 season. Fox was fired one year later, with a 12-4 regular season record — and a first-round playoff loss.

Arians, 65, compiled a 49-30-1 record in Arizona. But the Cardinals, once considered a rising power, missed the playoffs the last two seasons when they were 7-8-1 and 8-8.

Pagano, 57, spent six seasons in Indianapolis but was out after the Colts this season slumped to 4-12. Del Rio, 54, lasted only three years with the Raiders, who made the playoffs last season with a 12-4 record. But this season, the Raiders (6-10) faded badly and were never in serious contention for a postseason berth.