Cathy Boone, a homeless woman in Oregon, died with a bank account of $800,000 from an inheritance. They "couldn't find her". NOW WhAT?

When money lies dormant in a deposit account or appears to be abandoned, the bank or other organizations with which the money was deposited aren’t necessarily allowed to just keep that money for their own use. After a period of time, they’re required to turn it over to the state. This is called escheatment. Once it's turned over to the state for safekeeping, the owner of the money can still access it by making a proper claim for it.
The amount of time that passes before the account will be turned over depends on the state. Each state has different periods of time and other requirements for escheatment. The amount of time also depends on the type of money or account that’s being escheated. Bank accounts, checks, and wages may be subject to different periods.

All states require financial institutions, including brokerage firms and transfer agents, to report when personal property has been abandoned or unclaimed after a period of time specified by state law — often five years.  Before a brokerage account can be considered abandoned or unclaimed, the firm must make a diligent effort to locate the account owner.  If the firm is unable to do so, and the account has remained inactive for the period of time specified by state law, the firm must report the account to the state where the account is held.  The state then claims the account through a process called "escheatment," whereby the state becomes the owner of the account.
As part of the escheatment process, the state will hold the account as a bookkeeping entry, against which the former account owner may make a claim. The state routinely sells the securities in escheated accounts and treats the proceeds as state funds.  When a former account owner makes a valid request, however, the state will normally provide the former owner with cash equaling the value of the account at the time of escheatment.  This amount of cash does not include any dividends or interest covering the time after escheatment.

It's by no means a rare problem even if that case was unusual for the woman having all that money and no home.

I don't know the details of UK law in this, and I have not seen that word "escheatment" previously so perhaps it's not used over here; but it is common to see small-ads appeals in our local paper from one law firm or another, seeking anyone with rightful claims to the estate of someone who has died intestate and with no obvious relatives around.

If it remains unclaimed it does eventually go to the Treasury but I don't know if later claims can be entertained.

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My sister started work  many years ago in the office administering local burials and cremations. She reported that under her desk was a supermarket carrier-bag holding a few scruffy odds and ends and bits of clothing. This was the known "estate" of a homeless man who had died on the streets, and been cremated on the rates, and the Council were now trying to trace any family. As far as I know they never succeeded.