(Professional coin & currency nerd here)

They’re illegal not because of a law but because they were never issued for public use. They were used (briefly) for internal treasury / fed transfers. (Sort of like the mythical trillion-dollar coin that gets talked about every time the debt ceiling conversation comes up).

Because they were never issued privately or meant for use outside of the treasury system, if an individual were to own one it’s because it was stolen or otherwise improperly taken from the treasury.

There are rumors that a few exist in private collections (and I’ve heard of one a single degree away from me), but I’ve never seen it or confirmed that it’s anything more than a rumor.

There is one in the Smithsonian national collection however, and if you get an appointment to view the collection you can see and hold it. Pretty cool.

Somewhat vaguely related to this, not all bank notes in the UK are made equal. Good luck getting someone in England to accept an Ulster Bank, Danske bank, or Bank of Ireland note, despite them all being pound sterling notes issued in the UK worth the exact same amount.

I wonder: if these are essentially just a “paper trail” for deposits made at the BoD by issuing banks, why bother with a physical banknote at all? In the case of an insolvency of a bank, the bank’s notes would still continue circulating, after all.