There are a few examples of what you're talking about, but I don't really think they are analogous to Tennessee for various reasons.
Coach O went 10-25 at Ole Miss, then not counting his interim stint at USC resurfaces 9 years later at LSU and wins a title in year 4. Not sure that's analogous because of the big time gap between different HC jobs.
Saban's first HC job was a one-year stint at Toledo in 1990 where he went 9-2. 5 years later he showed up at Michigan St and went 19-16-1 his first 3 years. Similar to O there were big time gaps between HC stints at multiple schools. However, after year 3 at Michigan St or when he took the LSU job, there was absolutely nothing that indicated he was going to be a great coach. In fact I remember a lot of head-scratching with LSU hired him.
Mark Dantonio had 3 pretty mediocre Cincinnati teams, then went 22-17 his first 3 years at Michigan St. Not great, but not terrible either, and like O and Saban he switched jobs.
Johnny Majors was mediocre at Iowa St, and was actually mediocre at Pitt until his final year. At Tennessee, we were exceedingly patient with him, as it took almost 10 years to get the program running, and I don't consider him to be a truly great coach anyway.
Kirk Ferentz was terrible early in his career at Maine (12-21), then didn't get another HC job until Iowa came calling 7 years later. His first 3 years at Iowa he was 11-24; however, at least he got better each year and went 11-2 in year 4. This team is going backwards under Pruitt in year 3. Also, similar to O/Saban/Dantonio, there were time gaps and switched jobs.
Frank Beamer was nothing special his first 3 years at Virginia Tech (disregarding his previous job at I-AA Murray St), and he also struggled mightily his first 2 years after Tech entered the Big East, but he was also building a program from nothing. Not really an analogous situation.
I'm sure someone will point out Dabo, but none of Dabo's teams have been downright terrible like Pruitt's have been. And the team he coached during his 3rd full season won an ACC title, so not analogous.