It would obviously depend on the airline and the FE's qualifications. At the majors over here most of the FEs hired in the 70 through the 90s were pilots and the FE seat was first stop in their airline career they moved to a window seat as the two seat aircraft came on line. For the PFEs, those without a pilot license, it would be a different story. I know one PFE at brand AA who moved to the training department. Most airlines gave them priority for other jobs they were qualified for but many ended up out on the street.
At a prior job many of the FEs were pilots who had reached 60 years of age. We called it our retirement program to move back to the FE seat. They finally had to give up flying, whether they were ready or not. At the current job when we parked the Classics the company gave them the option if they could get 500 hours pilot time they could apply for a window seat. Some did, some didn't.