My understanding was that Robinhood was basically out of money to put up as collateral. What happens when a bank or broker announces that they are out of money?

My understanding was that Robinhood was basically out of money to put up as collateral. What happens when a bank or broker announces that they are out of money? Historically, there were runs on them as customers tried to pull their money out to prevent being left with a worthless IOU. Now, that is now how things actually work, but I could easily see such an announcement causing that.