What about this: Attila captures and sacks Constantinople after the earthquake of 448 A.D.
It would probably look like the sack of rome in 410, as you implied, meaning a relatively ordonned plunder looking more like a forced and harsh tribute, than "blood, death, vengence".
Now, even weakened by the earthquake, the walls remained a really big obstacle for anyone if they were correctly manned.
Which allowed the walls to be not only repaired but
completed by outer fortifications in mere 2 months.
I don't think it would give nearly as much leverage for Huns to breakout the fortifications (and let's not even speak about Hunnic siege capacities) which is why Atilla eventually never really went for Constantinople IOTL, and why Theodose eventually choose to move a large part of balkanic army within the city after the Roman defeat at the
River Utus.
You'd need a PoD with a catastrophic failure of Imperial authority early on in Constantinople, IMO, to allow the city to fail before Attila.
That said, while not overly obvious, we could see a TL where Attila manages to make a bet by arriving before Constantinople's authorities manage to fill the planned reconstructions and threatening enough the city (more trough fear rather than real power to do so) to recieve a big tribute and concessions (probably the same than he obtained in 449, that said).
But giving Theodosius was more or less murdered for being far too conciliating with Barbarians...I doubt it would recieve much support, so while it's less implausible than Atilla taking over the city, it's still asking for inner troubles as a second PoD to really work.
I don't think it would destroy the Empire, even with a relocation, as Eastern Romania enjoyed a better geostrategical position than its western counterpart, especially at this point.
Eventually, Hunnic strategy was less, like the other Barbarians, to carve out a foedi and monopolize the imperium on these regions at their benefit, than your usual steppe empire policy of plundering and clientelize everything in sight if it was worth it. The IOTL concession of a border south of Danube representing a week-day move was less a tentative to swallow up the ERE than making such plundering and tributary the easier, for exemple.
In this perspective, you could have Balkanic peninsula being raided at will, as long Eastern Romania does control the wealthy Syrian and Egyptian regions, it would stand.
Not that it wouldn't have consequences, especially a really important crisis about imperial legitimacy and authority, but while it was really a problem with Honorius and Valentinian's death because it was only one factor (if leading one, IMO) of the political crisis, ERE would survive this as most of its non-European provinces would be fine, and ERE still have a strong fleet to prevent anyone to really cross the sea even in the Bosphorus.
If Huns were managable by an WRE barely able to walk on its own legs, it was certainly so for ERE.