If a driver is terminated by their CSP but not disqualified by Fedex, they are free to be hired by another entity. I have to wonder why FXG wouldn't push the DQ on someone for route abandonment though, and why another contractor would want to take a chance on someone who did that... Is there more to this story?
As for cursing out a customer; unless there is proof of that happening or those accusations are a trend for a particular individual, it isn't likely anything that anyone is willing to act on because it is a "he said, she said" hearsay scenario. Have you ever been accused of being rude to a customer when you weren't, simply because they were irate and you couldn't help them? Happens all the time across many industries.