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Stability of a Broker: What if your broker goes bankrupt? Could you lose equity in your account?
Look at the link to the SIPC. I don't know exactly what you mean by "runs out of funds," but the SIPC will replace shares of stock stolen from your account, and up to $100,000 in cash.  The real risk is when a shady brokers sells you shares in a stock that becomes worthless, that's when "buyer beware" kicks in. No help there.