Southern Miss fired a coach who had been there 17 years and had produced winning seasons almost every year. They're a dumpster fire now.
New Mexico didn't fire Rocky Long, but he could read the writing on the wall and got out while the getting was good. New Mexico has yet to recover.
Both of those programs are relevant to BYU's situation because, unlike Ohio State and Florida State and other big-name programs that routinely fire coaches, there is a limited pool of coaching talent available for them to choose from.
But if you want an example from the Big Boys, look what has happened to Tennessee after they dumped Phil Fulmer....