In the case of a typical war of conquest, fighting pretty much stops as soon as one nation surrenders. However, no nation state in the world asks, 'How can we save the most lives?', instead asking, 'Do we have enough people to send to their deaths to potentially preserve our monopoly of power?'
Of course, at the beginning of every war, some people genuinely believe that joining and defending the nation they live in is in their best interests, but these numbers quickly drop over time. As history and current events show, states start to use forced conscription in every prolonged war at some point.