Lets say I have $5k in my brokerage account and I buy a 100 shares of $50 stock on a 4:1 margin. So I put up $1,250 leaving $3750 in the brokerage. 5 minutes later the stock plunges to $4/share and I am down $4600, which I can't cover in the brokerage. What happens? Can I be in debt now to the brokerage? Or will they automatically liquidate my position?
Different brokerages have different house rules for margin requirements and margin calls. You will likely get a margin call giving you a small amount of time to deposit the required funds to bring your account balance up to the required margin requirements. In reality, a stock that falls from $50 to $4 in a short period will probably become unmarginable. In short, yes, you will owe the broker for the loss.