A POD around 263 or 310 would be when Chinese civilization was at its absolute weakest and most vulnerable, but by then most of the neighboring tribes had started to assimilate into Chinese culture and even with most of the population dead (that was one of the bloodiest periods in history seeing 60-80 million people get reduced to less than 15 million and the decline further with genocides that make the Mongols seem pleasant) (regular sacking of cities, mass imprisonment, regular death, sweeping famines, that kind of thing) the invading groups adopted Chinese language, mannerisms of state, and simply were absorbed into it.
Western Rome, or Roman in general, never went extinct. Its culture shattered and diverged, its language shattered and declined in some areas while rising in others, and the idea of rome is still very much alive in Italy, Greece, and Romania. Yes. Romania. The name itself is Rome. Even when the last bit of it was defeated by the Turks we had the Holy Romans, Russians, and Ottomans claiming political and cultural continuation of the damn thing. Hell, the Vatican is Rome in some regards. It didn't die.