Is this a run-on sentence?
The Scythians were nomadic warriors who lived in Central Asia in the ninth century BCE, before disappearing during the second century CE, they had spread westward into Eastern Europe.

 - no
 - yes
This is a run-on sentence. It is a comma splice formed from two sentences run together, joined by just a comma.
The Scythians were nomadic warriors who lived in Central Asia in the ninth century BCE, before disappearing during the second century CE, they had spread westward into Eastern Europe.
Here is one way to fix the run-on sentence:
The Scythians were nomadic warriors who lived in Central Asia in the ninth century BCE. Before disappearing during the second century CE, they had spread westward into Eastern Europe.