This sounds a little off since Roman citizenship expanded until 212 when it was granted to all free men in the empire. But perhaps she was talking about the failure to absorb "barbarian" tribes that came over the border later, that wanted to become Roman and sometimes thought of themselves as Roman.

The sack of Rome in 410 was a shock, but the end of the western Roman empire later that century probably wasn't understood as such at the time since they didn't know that decentralization would be permanent; after terrible civil wars, another emperor would usually reunite the empire. And even much later there were often claims to be a continuation.

Contrast with China where new dynasties would rise after the old one falls.

> another emperor would usually reunite the empire

Well he did, in the 530-550s to a significant extent. That of course didn’t work out because of the plague, climate change and other factors.