Will Lloyd's of London really insure brokerage accounts up to $49.5 million?

(EDIT: This answer is based on the fundamentally different original question.)

Will they really replace the entire investment up to $250M ?

You snipped out the part that answers your question.

https://investor.vanguard.com/investing/account-protection "This coverage has an aggregate limit of $250 million for all claims of securities and cash and incorporates a per client coverage limit of $49.5 million for securities and $1.9 million for cash."

What exactly are these terms and conditions (and how easily will they change them) ?

Ask Vanguard.

Who are these "Syndicates" and why is it not just Lloyds ?

https://www.investopedia.com/terms/l/lloyds-london.asp

"Lloyd's of London is a British insurance market where members operate as syndicates to insure and spread out the risks of different businesses, organizations, and individuals. The syndicates are specialized in different types of risks and each syndicate decides which type of risk to insure. The main purpose of Lloyd's of London is to act as an intermediary between clients, underwriters, brokers, and insurance companies.

Will they really replace the entire investment up to $49.5M?

Probably not because there's an aggregate limit of $250mm. I suspect the way it works is people with assets in excess of the SIPC coverage could recoupe some sort of proportional loss up to the $250mm aggregate but never more than $49.5mm.

What exactly are these terms and conditions (and how easily will they change them) ?

Probably just ask Vanguard. In sure the contract has some in-force window after which contract terms can be changed.

Who are these "Syndicates" and why is it not just Lloyds ?

Because any time anything is "insured by Lloyd's of London" its actually spread out over multiple Lloyd's syndicates, that's how Lloyd's works. The certificate of coverage will illustrate what percentage of the risk is attributable to each syndicate. In the early days of the Lloyd's market the syndicates were wealthy individuals/families now many syndicates are large reinsurers.

Any examples of how this played out in the past?

Probably not. Lloyd's is a reasonably prominent excess insurer, providing additional coverage on top of some other existing coverage or covering more obscure risks. Lloyd's definitely covers risks and pays claims, I'm just not sure how many situations have ever existed where there was an SIPC covered event AND SIPC coverage was exhausted AND that broker had excess coverage. Maybe ask Vanguard. To that end I'm not sure how many dollars have ever been recovered by SIPC in the first place.