Ok heres the first scenario:
In 1940 Germany invaded England and took it over… Churchill and the British people fight from her colonies and from their additional troops and equipment are constructed. Do you think for a second that if england falls … thats it… they just roll over and cry uncle Adolf? NO they fight on from their colonies where much of their support comes from. Only the people on england now have a different fight as you stated … as partisans…
If Moscow falls Stalin takes the train to Gorki or Kazan and fights from his base in the Urals. The ability to raise additional troops is not encumbered only in the respect that Stalin still has factories and a population to draw recruits from. Once all the factories are gone its a completely a different matter… no equipment = no army. thats the key difference.
If Canada, India, Australia, have fallen then i would agree with you. these colonies are all part of the roots of the British Empire. They are interdependant economically and militarily. Capital falling as a means to conquer a nation is a fossilized concept that is better regulated to a “romantic war” like WW1. Of course it has some effects but a modern nation is not that dependant upon one or two key cities.