I can think of several unusual job-ending, but not career-ending, incidents. They're all a little on the humorous side.
Here in Atlanta, Frank Jaxon was the last PD of Z93 before the flip to Dave-FM. A memo about the format change, that would take place that afternoon, was leaked out via email. The email stated Michelle Engel would be the PD of Dave-FM. AJC radio writer Rodney Ho telephoned Frank Jaxon and said, "So Michelle Engel is replacing you?" Jaxon responded, "Michelle who?" I guess Jaxon got confirmation that he was out pretty quickly after that.
In the 1970's, Tom Dooley was afternoon drive personality on legendary Top-40 KHJ in Los Angeles. He disliked living in L.A. and working there. He accepted a position in Louisville, but his KHJ contract was iron clad. So someone suggested he say something on the air that would force management to fire him. So after a song, he said something like, "I believe President Nixon and others in his administration should be tried for high crimes regarding the assassinations of Martin Luther King, Bobby Kennedy and others." And then, he repeated it. That was the last thing he ever said on KHJ. Rumor was the his wife was waiting outside the station in a van that had already been packed for their move.
Then there was the famous WABC/NY firing in the 60's. Midday personality Bob Dayton said, "Monday is the anniversary of Hiroshima. So in honor of that...and he started the song "Sixteen Candles," which begins with "Happy birthday, baby." That was the end of Dayton at WABC.
The other famous WABC incident was after Roby Yonge's contract wasn't renewed, they let him go on the air to finish out his current contract. On the overnight show, he turned WABC into a talk station, discussing rumors of the death of Paul McCartney. PD Rick Sklar was notified, and Sklar came to the station in the middle of the night to remove Yonge.