Yes, you will owe your broker.
You might think “how can that happen? Won’t they just close my positions automatically if my margin falls below the required level?”
The answer is, yes they will do that if they can. But sometimes the market moves so fast or gaps completely that they are not able to close out your positions in time, and that can lead to big losses which may exceed the balance of your account, which you are liable for.
Probably the most famous event recently where this happened was in January 2015 when the Swiss National Bank, without any warning, announced it was abandoning its Euro cap policy (which kept the value of the Swiss franc artificially low). The SWF immediately soared in value, gaining an incredible 30% against the Euro in less than 2 hours.
Great if you had a long position in SWF, terrible if you had shorted it. The surprise announcement led to a lack of liquidity that meant positions could not be closed out fast enough, and some ordinary traders, even with modest short positions were suddenly left in hundreds of thousands of debt.
One teacher who had a small, short position was plunged into £280,000 of debt by the adverse move. IG (his broker) did not forgive his debt or anyone else’s who were adversely affected by the move, and several lost their houses, were made bankrupt etc.
https://www.google.com/url?sa=i&sou...aw1g-3HyBokBUl47lErXRu2A&ust=1546221877003911
HOWEVER, some brokers (mine included) offered ‘negative balance protection’ which means that you can never be liable for more than the balance of your account.
The new ESMA rules, much maligned for their ridiculous leverage caps, do now require regulated brokers to offer Negative Balance Protection to all of their retail clients, a sensible protection in my opinion. So if you trade with an EU regulated broker (as a retail, not professional trader) you get this protection as standard.
But if you trade with a broker outside the EU (eg some of the Australian brokers which are becoming very popular due to their non-ESMA leverages) then you are vulnerable to gapping or other adverse movements putting your account into the negative, unless they specifically offer negative balance protection.