The fds may come out of view for many reasons but i dont think after an engine failure.
In any case switching the other side fd off makes no sense at all.
The only time the PM fd would be out of view in normal ops would be during an ILS with DME located on a VOR.
IF an eng fails, does the respective FCC fails, or does it get powered from the opposite side because of the BTB.
So if you lose an engine,both FCC still have power but the opposite engine FCC is normally used.(ie eng1 failed,A/P B engaged to avoid possible redisengagement.)
The FCC are electrically powered and as long as your transfer bus works,both will still be powered and available.
If FCC fails does the FD also fail or is it independent of the FD.
If an FCC fails,its Fd will go out of view and the FD flag will annunciate on the PFD.
and mostly if a loss of a sing gene, does the FCC fail, or only the auto pilot? and of the BTB closes, can the autopilot be re engaged on the failed engine side or no...
The Auto pilot will disconnect and the associated FCC will not send signal to the flight controls actuators but STILL available after power is restored on the associated gen.