Its an interesting question. It also depends on how centralised the nation is, and how cohesive its 'cores' are. France, for example, could probably survive as a rump if it lost Paris somehow, with an exile government perhaps setting up in somewhere like Marseilles or Bordeaux. They'd probably fall into extreme unrest and poverty would skyrocket in the ensuing chaos, but the French wouldn't stop being the French. The French state wouldn't cease to exist. Even if the French were driven out of France, there's a good chance of French colonial regimes clinging on, although those could then splinter into different states.
There could perhaps be some kind of 'state gravity' mechanic, where the peripheral regions are only held together by the nation or empire's core being stable enough. If things deteriorate too badly at home, you could start to lose protectorates as rival administrations set themselves up, and eventually the whole thing could just splinter and collapse into a bunch of successor states. That's not even getting into revolts by native peoples now that there is no centrally maintained army and navy to prevent such things from happening.
I'd like to contrast France to, say, Austria losing Austria or the Ottomans losing Istanbul. But I realise that I don't know as much about Eastern Europe during this period as I'd like to, so others will have to take up the mantle while I do some belated research.
