Back in the early 90s there was an angle where Rick Rude was insulting the Big Boss Man's mother. It went on for a while and then he was “fired” for it.
Was there actually going to be a pay off to this or did they just know Rude was leaving and wanted an excuse?
A bit of both. It was leading to Rude/Bossman at Wrestlemania as originally planned as far as I know, but Rude was injured and they kept advertising him in main events at house shows anyway. Rude argued that if they're using his name to draw the house, he should be paid main event money for those shows, and when Vince disagreed, Rude told him where to stick it and quit.