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?
If the price had dropped to $4 from $50, and you had $5000 to start with on your account, you will be left with $400 in your account if you closed the position now. So you would not be in debt if this was the only possition you had open.
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.