It depends on the company, but as a rule you would be given the same amount of shares at a price of 0. Theoretically the stock price should halve, so you would maintain the same amount of equity at the same average price, albeit with a large running loss on one and a large running profit on the other leg.
Alternatively, a company might double the size of your trade and halve the opening level, although I don't find this nearly so transparent.
Sadly you can;t make money by shorting a stock and buying back the same size immediately after the stock split...