Contingency fees based on what you can save the client - "reverse contingency"?

You are representing a client in a contract dispute where the opposing party claims he is owed $10,000 for services rendered. The client likely will not be able to pay your hourly rate to handle the matter. Can you enter into a “reverse contingent fee” agreement whereby you will be entitled to a percentage of the money that you save the client?  ETHICSearch has published a short article explaining why the answer is yes, as long as the fee is reasonable, of course.