I was reading a bit on the ancient contact between the Byzantine Empire (known to the Chinese as "Fu-lin") and Tang/Song China. I know that in the Late Roman Empire, several envoys were sent to the Far East with varied results, but with the loss of Egypt and Syria in the 600s, contact between the two Empires dwindled almost to a stand still. I believe the Chinese report something like "Da-Qin is no more, and has been replaced by Fu-lin" or something along those lines.
However, there is often a mention that a Byzantine envoy was sent in the 11th Century and reported by the Chinese sources. I am not aware of any reports of this in Byzantine sources, but it would be interesting to hear what the Chinese say about this envoy. Might anyone be able to elaborate on that?
I know it's a bit of a source overload, but this page has a series of reports from Chinese sources on Byzantine embassies/relations/affairs, with two accounts in particular of an embassy in "the sixth year of Yuan-yu [1091 CE]." It looks like it's mostly details of what the embassy brought with them (cloth, precious metals, etc.), but hopefully it might be useful for you!
Yea I actually have some scholarly articles that talk about this subject, including a relatively recent one in 2005, "A study of Byzantine coins discovered in China and related problems."
The sampling of coins found drop off entirely after the crisis of the 7th century, which is indicative of the collapse of Roman power in the eastern mediterranean after the Arab conquests. Although I know there are descriptions of Byzantium from the Chinese perspective, most direct and recorded contact with the west was mediated through the Caliphates and their Islamic successor states, considering their proximity and relative power in comparison to Byzantium. Famed Chinese historical linguist Pulleyblank always cautions against taking too much at face value of Chinese descriptions of the Roman Empire, as the Chinese viewed Rome as a mythical "nega-China" than any actual state. We should simultaneously caution whether these descriptions of the Byzantine Empire, they had any inkling of the continuity between Byzantium and Rome, or they simply viewed them as among the multitudes of western nations beyond their horizon.
The line you're thinking of, was actually a Sogdian report talking about the collapse of the centralized Chinese state (not the Roman state) in the Early Medieval/Age of Disunity/Six Dynasties period.
“The last emperor, so they say, fled from Luoyang because of the famine and fire was set to his palace and to the city, and the palace was burnt and the city [destroyed]. Luoyang is no more, Ye is no more!"
To the best of my knowledge, I don't believe there is any direct recording of contact between Europe (including Byzantium) and China until the Mongol invasions united enough of central asia to provide overland transit.
Doesn't mean there weren't any, but I believe the records as well as the political interest (namely that Byzantium was not of direct trade interest to China in the same way as the Islamic states) were not aligned for such trips to be made worthwhile.
EDIT: Although with that said, what book has that mention of a Byzantine envoy to China?