But then again, did Rome really fall, in a culturally sense. Yes the political system fell, but culturally Rome lived on. The barbarians we picture as animal skin wearing brutes, but in reality they were people who fully embraced Roman culture. So if the Goths, Vandals, etc considered themselves part of Roman culture, did Rome really fall.
Actually, the Romans “moved” to what is now Turkey—the Byzantine Roman Empire centered on Constantinople, and kept on going for quite a while longer, although of course you could say at that point they were more Greek than Roman.