That is basically one of the conspiracy theories I have heard related to central bank digital currencies.
As the tale goes, eventually major banks will run into another financial crisis (possibly intentionally if you really like conspiracy theories). The government will say they have no choice but to step in, and their solution will be to open the federal reserve to the public as a government-run bank. All funds lost in the crisis would be covered under an extended FDIC program and the money would be waiting for you in your new Fed bank account, denominated in the newly created CBDC.
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In no way am I vouching for the theory, just sharing it as it is very relates to you question of how it could be handled.
The weirdest problem I see with this conspiracy theory is that I don't see the actual conspiracy?
Like, USD is a fiat currency, it's backed by taxes. The only difference between a paper dollar in your hand, a dollar in a traditional bank account, and a dollar on the hypothetical FedCoin blockchain is how easy it is to spend, what gatekeepers are involved, and what anti-fraud/anti-theft tools you can avail yourself of. Moving from a traditional bank account to a CBDC doesn't make it any easier for the government to seize your funds - they already can do that just fine with basically anything.
I believe the conspiracy portion of that theory is that the financial crisis would be triggered, or allowed, intentionally to create the excuse for a CBDC and fed bank.
I don't see it as likely, just a theory I've seen floated.