I am thinking about the idea of a tv show about a roman soldier just after the fall of the roman empire who is struggling with the fall of the relative safety of the vast roman empire. He then tries to reach the Byzantium empire, hoping to find some stability there, moving through Europe falling apart. I was wondering, is there any documentation of people who haven actually tried, or even suceeded, while doing this?
I'm afraid this answer might be a bit unsatisfying. The collapse of the Western Empire did not happen very suddenly. The Goths had been within the empire for roughly a century and the Vandals about 70-80 years there were no Romans alive when the west "fell" that could likely remember a Time when some germanic group or another wasn't "squatting" on Roman territory. As often as not these groups were administering Roman territory for the imperial government and fighting on behalf of the Empire as they were fighting with it. Even in 476 when Romulus Augusts was deposed and Odoacer became king of Italy, it wasn't all that different from the Visigoths or Franks whose kings were nominal subjects of the Emperor and administered the provinces on the emperors behalf. Odoacer would even mint coins in the Image of the ex-western emperor Julius Nepos until Nepos' death, though we would let Nepos return to Italy..in fact for the next couple centuries the western kingdoms would continue to Mint coins displaying the image of the Eastern emperors. So the western empire didn't just disappear one day, to the perspective of someone living at the time.
The educated elites would be most likely to know about they changes going on around them than your average poor farmer but the difficultly if travel for people and information and the long amount of time that can take, nevermind the potential unreliability of that news might have meant that the further away from Italy you got the less even an educated Elite might know for certain. Plus the wealth of the elites in ancient times was in land, so even if Theuderic the Frank shows up at your door and says; "hey pal, half your Empire is gone and you're gonna be paying your taxes to us now," you can't just trade your land in for a chest of coins and ride off for Constantinople. For poor Publius the cobbler in Tolouse he might not even know that anything had changed, Sure he was paying the goths taxes, but the coins still have the emperors face on them, and besides he'd been paying the Goths taxes for as decades as far as he can recall. The Gallo-Roman Aristocracy, their Iberian counterparts, and the Italian Senatorial class all for the most part just made accommodations with their new Germanic overlords and went on with their business. We do hear that under Justinian some Italian senators and other elites fled east, but this was due to the devastation from the Gothic wars which ruined Italy far more than the "fall" of the West 70 years earlier.
sources: "The Fall of the Roman Empire: a New History of Rome and the Barbarians" Peter Heather
"The Fall of Rome and the End of Civilization" Bryan Ward-Perkins
"Byzantium: The Early Centuries" John Julius Norwich
I've probably left out a couple good sources too and I'm sure there might be a few salient examples of western "emigres" but nothing really springs to mind, and I'm happy to be corrected, I've been up for 19 hours as I type this.