You are making a sense here and that is what some would do immediately they get hold of the wallet they are about to recover the fund insider. Some can even tell you that the previous agreement will be invalid due to the continuous efforts that is put together to recover the fund.
Everyone has to be very careful about some recovery services since they can suddenly becomes greedy and would want to take huge amounts of the funds available in the wallet, contrary to the initial agreement. Greed is already part of the human faculty and some people don't waste time to utilize when they are in possession of clients funds. Transparency is what will make a difference in this kind of services.
Only inexperience service renders will act this way. If an agreement has been made from the beginning, there is flexibility for changes incase needs for it arises. Perhaps due to the difficulty level to restore the wallets, they can striker a new agreement to make conclusions. The reason why I say there should be flexibility is because most times customers dont even know where to start to explain what they need to do, some of them claim they have the necessary details in the end they cant provide it. So communication is the key here. Both parties should communicate and agreement should be made flexible.