The company doesnt have to go to zero, but your options account equity can easily do that. Even options on very safe things like, say, MSFT/GOOG/AMZN/SPY/BAC/VZ/etc can lead your account down to zero, and it mostly depends on how leveraged you are.
Suppose you sold puts on Verizon at 55. You are on the hook to buy Verizon at 55. If you have 5500 in equity, you're fine. You get the stock and hold it, perhaps wheel it.
But if all you do with $5500 in account equity is sell a single put contract, you wont make much money. So most people sell more than they have equity to support. So perhaps you sell three Verizon contracts. Your $5500 in account equity is now on the hook for 3*$5500. If Verizon stock goes down to 36, you are wiped out.
Oh, and all this while, you arent capturing any of the Verizon upside either! You only get the premium.
