If you buy a stock with leverage and the value of your holdings go below zero, do you still own any shares?

For example, If I bought 100 shares of xyz using 2:1 leverage, so I would have actually only had enough money for 50 shares. But if I purchased these shares and then the price fell to where the value of my holdings was below zero, would I just loss it all right there even if I didn't sell out. If I held the stock and one day the value went high enough to make a profit would I still own those shares??

That will never happen. First the value of your stock can not go below zero. Second, when you buy stocks on margin, your broker will protect his interest. If the stock drops in value below the required maintenance margin level, you will get a margin call. If you do not deposit additional funds or sell the stock, your broker will sell it for you. The margin agreement you sign gives him permission to do that.