No. The broker won't allow you to lose more than the available funds on your trading account. It will simply close your losing position when the resulting account balance becomes too close to zero. The loss that is bigger than the trader's deposit is a direct loss of the Forex broker. It's in the brokers' interest to prevent such losses. To secure themselves brokers implement a Stop-Out level (usually about 20%), which means that the most losing position will be closed once (free margin / used margin) * 100% becomes equal or less than this level.
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