User blog comment:Bato of the Heavy Iron Rock Hammer/What happens to the Alvarez Empire after FT's ending?/@comment-7418318-20170723004500

Seems the final chapter did partially clear this issue up.

The Alvarez Empire still exists and is in a stable enough shape to have formed a peacetreaty with Fiore.

If they were able to hold out for several month or maybe even a year after the death of their Emperor, I think it's save to assume that the other continent didn't devolve into pure chaos and civil war. There might have been conflicts, but apparently nothing big enough to end the country as a whole.