Victorious armies, after destroying an opposing army, would usually pillage the enemy city, etc., since nothing stood in their way. In the case of single combat, however, the opposing army is still there to provide resistance to such acts. Would the winning army still attempt to obtain loot in certain ways? Would the losers instead owe them a tribute? If a battle were decided in single combat, would the losing army graciously surrender, and the victorious army, in turn, subjugate the losers in a (relatively) gracious and nonviolent manner? How did the populations react? What was the scale of the largest conflict resolved by single combat?
Just to be clear, at least in the period I study (ancient Greece), there is no record of any historical conflict that was resolved by single combat. The idea only occurs in stories, usually set in a mythical past. Moreover, as I've explained before, even in these stories the single combat never actually resolves the conflict, since the outcome is always disputed and further violence usually follows. It is possible that single combat was once practiced as a way to minimise the damage done in war, and these stories preserve a hazy memory of that practice; but if so, they also demonstrate why this form of conflict resolution went out of style. When we get to historical times we only have one example of a prearranged duel between 300 men on each side, but this experiment also failed because the outcome was not accepted.
But in any case, the entire point of reducing a war to a fight between two champions is to channel its course and establish conditions of victory and defeat that avoid putting the entire community at risk. In other words, single combat is a form of negotiation, not a form of total war. If the two sides can agree to a time, place, and set of rules by which their conflict will be decided, they can also agree on the terms of the outcome. By definition, these terms would have to be limited; the purpose of single combat was to place the rest of the community out of harm's way, not to make their lives wholly dependent on a single duel. If the terms proposed by one side were as existential as those of regular ancient warfare, no community was likely to accept them as the outcome of one fight between two people.
Take for example the duel between Paris and Menelaos in Iliad 2, the most famous attempt to resolve a (mythical) war by single combat. The proposal is that the two men will fight over who gets to take Helen home, but the rest of the Greeks and Trojans will make peace and be friends. The duel isn't just meant to determine how the outcome will be reached, but also what that outcome is; it explicitly exempts the city of Troy (and the Greek army) from further violence. Should one side break this agreement by going after anything beyond Helen and her dowry, then of course the other side would not be obliged to sit idly by. Their weapons are still in their hands and they are prepared to fight for anything that isn't stipulated as part of the terms.
And indeed, when Athena persuades Pandaros to violate the truce by taking a pot shot at Menelaos with his bow, the armies go straight back to all-out fighting, and the stakes revert from the fate of Helen to the fate of Troy as a whole. This is generally what happens after these attempts to reduce war to single combat; whatever the outcome, either violations of the truce or foul play would be cited as a reason to return to the full-scale violence that was always the norm in ancient warfare. In the historical period, the only known examples of single combat don't actually come with any terms attached; they just served to display the valour and spread the glory of individual fighters, but were never assumed to resolve anything, and were ultimately abandoned as an old-fashioned bit of showmanship.