Tennessee is the gold standard for this. With both Bill Battle and Fulmer. Battle wasn't recruiting worth anything at all. The program was in bad shape his last two years and horrible shape when Majors arrived.
Fulmer should have been let go in 2005. There were plenty of very concerning flops before that season in 1999 and 2002. Recruiting fell apart. Cutcliffe was a band-aid on a gushing wound. We didn't have any OL or DL depth left at all when Kiffin took over. That senior class graduating was a factor in Kiffin's exit for USC. He knew he wasn't going to be competitive for a few years and wanted to get while the getting was good. Dooley didn't recruit the positions well either. Butch seemingly recruited them well, but we've seen no player development at all from him. So here we sit.
Probably the other best examples have been mentioned, Penn State and Florida State but it's hard to get a legend off the sidelines without a major scandal.
Teams who pull the trigger quickly are usually rewarded eventually. Alabama being a prime example. They fired Ray Perkins after a 10-3 season. Then doubled down and fired Bill Curry after a 10-2 season. Stallings won the NC 3 years later.
Mike Dubose won 10 games and was kept but fired after 3-8 the next year. Shula won 10 games and was fired a season later. NCAA scandals were swirling at the time.
At the time Alabama was firing 10 win coaches who didn't win championships, we were giving Fulmer raises and extensions for 8 win seasons. Thus we are where we are now and they are where they are.