Did any sheriff had an exit? I can't remember.
Turk Tobias:
Although it was not mentioned explicitly, we were led to assume that Tobias was removed from office following disciplinary measures after the abuse of his office transpired in the inquest at the end of season 1. A few months went by off screen between the season 1 finale and the season 2 première, which is clearly indicated by the visible progress in Melissa's pregnancy, so there was plenty of time to remove Tobias from his office and instate Dan Robbins as the sheriff.
Dan Robbins:
We don't know what became of him after the end of season 4. All we know is that season 5 began six weeks after the explosion in the season 4 cliffhanger, and Gilmore was introduced as the sheriff more or less in a side note by the newscaster in the TV report about the investigation on the explosion.
Unfortunately, we have not found out yet why Joe Lambie left the show, but I reached out to him for an interview for falconcrest.org approximately 20 years ago, and I must say I've never talked to someone from the cast or crew who was so unfriendly, to say the least. While anyone else has been very happy about our continuous efforts to keep the memory of the show alive, Lambie was very rude, making it clear he was not just unwilling to talk to me, but was very pissed by the show and requested he never be contacted about "Falcon Crest" again. I'm pretty sure it was a contractual issue over which he was terminated, but I don't know any details. I asked Earl what had happened, but neither he nor anyone else I asked remembered. I later heard rumors that Lambie had expected his rôle would become bigger and that he and another actor repeatedly discussed if there was a possibility to bring in a female acting friend of Lambie's as another cast member. It's pure speculation these incidents might be connected, but I wouldn't be surprised if they were. Since we never publish rumors in our "Behind the Scenes" section (except in cases where we see a necessity for clarifying, denying, etc. in which case we expressly label the issue as a rumor), this never made it to the website.
Floyd Gilmore:
John Bennett Perry (by the way, Matthew Perry's father) left in the first third of season 6 to star in "Independence" where he also played the sheriff. He explained to me in a 2007 interview (which is not on falconcrest.org, but only in volume 2 of our "FALCON CRESTers Tell It All!" newsletter series) that it was not an easy decision, but it was too tempting because he was the lead, and the project was considered a pilot. It never became a series in the end though.
In the storyline on "Falcon", it was briefly mentioned in in a TV or radio report (in connection with Chase's election as the chairman of the county board of supervisors) that Jack North won the 1986 election over Gilmore.
Jack North:
He actually had an on-screen exit, telling Angela that he'd go back to New York in the first half of season 7.
George Buckman:
No mention of him after season 7. The new producers of season 8 apparently wanted a Latino sheriff (following Mike Filerman's preference for a more Hispanic touch of the show), hence the replacement, but there was no explanation whatsoever.
Sheriff Sanchez (the only sheriff with no first name):
No mention of Sanchez after season 8.
Jack Broom:
Like most of the new characters in season 9, he was just there out of the blue.