Your understand is wrong in practice. In fact a recent example in the US is the MF Global fraud. That is why there is the SIPC http://www.sipc.org/How/Brochur

Your understand is wrong in practice. In fact a recent example in the US is the MF Global fraud. That is why there is the SIPC http://www.sipc.org/How/Brochure.aspx http://www.sipc.org/How/Brochure.aspx it's like the FDIC except for losses related to fraud surrounding the failure of a brokerage firm.