Interesting question.
What's the short percentage? I suppose shares being sold short could be counted as held by two different institutions at the same time (the lender of the shares and the seller). This might work if you had an issue with essentially no noninstitutional holdings and a high short percentage. Hmmm....
That's a thought. I'm afraid I can't answer your question, though, because I don't have a specific example in mind at the moment. I have noticed just a few examples over the past few months, and it just occurred to me to post this today.
But in general, I'm nervous about buying a stock where more than 100% of the shares are... well, anything. And I'm also nervous about buying a high-yield stock when the dividend payout ratio is over 100%. But I think I have good reason for the latter nervousness, whereas I just don't understand the former scenario at all.