I sometimes reduce my position prior to the dividend coming into play. But that decision is impacted as to how much $$$ I'm up (or down) at that point in time. If I have a decent profit going I may stay short my entire position if I feel the stock will continue to act weak. Overall market sentiment also influences me some.
Cash basis tax payers don't have to report accrued dividends. It's only reported in the year actually received/paid. If received, it's dividend income reported on form 1040. If paid, as is the case if you held the stock short on the record date, it adds to your basis which reduces the amount of capital gains reported on Schedule D when the stock is purchased back.