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Depends.

Sometimes, when an empire collapses, those that pick up the shattered remains build something better and fairer for all. This is what happened after the Allies broke up the German and Japanese empires after World War II.

But the historical norm has been Balkanisation as the internal unity and peace that the empire once provided crumbles and the nations that arise in its wake squabble over the dwindling remaining resources of the dead empire. And since the empire is no longer around to enforce its laws, enable commerce, and keep the peace, what tends to happen is economic, scientific, and cultural regression as those that remain spend all their effort trying to take as many of the existing resources for themselves rather than creating more resources. That's what happened over the centuries-long collapse of the Roman Empire.