After the sack of Constantinople, much of that wealth, including the secret of silk-making was taken back to Italy, and the ERE would never recover from this.
For reference, the amount looted from Constantinople during its sack is meant to be around 900,000 silver marks -- enough to raise the entire Venetian navy almost 6 times over. (https://en.wikipedia.org/wiki/Sack_of_Constantinople#sack_of...)
Of course, a huge amount of wealth remained in the west, even after Odoacer's conquest (see this mosaic of the palace of Theodoric: https://www.worldhistory.org/image/3090/palace-of-theodoric-... which is in undeniably Roman form). That said, the ERE would continue to be the center of wealth in Europe up until at least the sack.
I think it's important to note that Odoacer, in destroying the WRE was not considered by his contemporaries to have destroyed the Roman Empire. He immediately sent the imperial regalia to the Emperor in the east and declared himself a Viceroy of the eastern Roman emperor. In this way, I think the ERE thought it kind of convenient, as they now, at least on paper had full control of the whole Roman empire. The identity of 'Roman' in the West was not broken, so I've read until the ERE decided to 'reconquer' Rome and mainland Italy for being barbarian, which, as you can imagine would throw your personal identity for a bit of a loop.
Despite still being greatly dilapidated when Constantinople was finally invaded by the Ottomans 200 years after the sack, it was still famous for silk. Mehmed The Conqueror is attested to have said, upon wandering its ruins:
The spider is curtain-bearer in the palace of Chosroes,
The owl sounds the relief in the castle of Afrasiyab.