Well, it would be stupid to trust the broker. What technically prevents them to run away with all stocks?
I currently manage it by simply having accounts with several to avoid putting all eggs in one basket. But this is hardly a solution.
Brokers (in traditional finance) are regulated, audited, and also are often subject to insurance policies in case they went bankrupt, or similar. If you are dealing with a large and reputable institution, you are unlikely to gain any benefit by assigning the shares to yourself I would suspect. Someone please correct me if I am missing something though.
It's called the law.
> Well, it would be stupid to trust the broker. [..] I currently manage it by simply having accounts with several[...]
If you believe it's "stupid" to trust brokers, spreading your exposure across several of them may protect against a complete loss. But it also increases the risk of some loss and, on balance, has exactly the same expected value. The law diminishing marginal utility may put your strategy slightly ahead, but the difference is similarly marginal.
SIPC insurance is supposed to protect you in case they run away anyway.
What protects a bank from running away with your cash?