When an empire falls and leaves no leadership, a power vacuum forms. This is when people fight for control of a specific area.
In Europe and China, after Rome and the Han fell, the trade governing the empires and law networks collapsed.
In Europe, this led to the rise of local, self-reliant, tribal governments and the early medieval manorial system. When the Han Dynasty fell in China, the empire was split into smaller kingdoms and even smaller independent landowners later.
Trade in China remained under threat from raids by Mongols and Xiongnu. In Europe, trade was limited to small trade relationships between manors.
Religion was a unifying factor in Europe and China at this time. In China, Buddhism became popular, while Christianity united communities in Europe.