One of the posts above infers that they were able to leave at the end of Voyager. Don't know if that's true or not. If it is, then why not leave? They had 12 months knowing that the seventh season of Voyager would be the last.
If the statement was false, then there are ways of maneuvering yourself out. I'll use the Straczynski example again. Refuse to take network direction. They either replace you or let you get away with it. If they replace you, you're freed up for other work.
Considering that Berman had overseen Trek for well over a decade by that point, I find it hard to believe that 1) he wouldn't be able to take a few months out to find other projects before he and his family were on the breadline, and 2) he would struggle to any degree to find work if he wanted it.