From The New Penguin Atlas of Medieval History by Colin McEvedy:
Not that the Germans had any thought of destroying the Empire: it had existed for so long that everyone assumed it would go on forever. What the barbarian warlords wanted was imperial grants and commissions, lands for their followers and positions for themselves.
McEvedy is describing the Western Roman Empire in AD 408. Rome was still culturally important and rich, but they had been relying on hired foreigners for so long that they had very few military men of their own. It had gone out of fashion for young Romans to become warriors; Rome had plenty of gold to buy the temporary allegiance of barbarians.
The Germanic and Gaulish tribes to the north were used to being able to alternately work for and attack Rome; they had no real loyalty to Rome but had grown used to Roman institutions being rich and easily manipulated. Visigoths sacked Rome in this period, not intending to hold (and feed) the city, but instead staying only for three days. Their move was intended to show Rome that they were serious about their demands for ransom.
The Western Empire was not taken seriously as a political force after this point, though Rome was considered worth sacking several more times during the fifth century.