Oh, I would not dream of suggesting they pay for the fanfic itself. I most sincerely apologise for any lack of fiscal clarity in the statement above.
No, merely monies for the time and labor required to facilitate the supply, in much the same way as fanfiction sites need advertising payments to cover site costs and allow hosting without making a profit from the intellectual property of others. As a busy filmmaker, raccanteur, beat poet, bounty hunter, and former child star Deathstalker would likely need to pass any request for supply of archived derivative works onto a PA or gopher who would then need to locate, attach to email and send on to the requestee. There'd be no profit made from the supply of the story, I'm sure, because of the legal dogs of war thence to be unleashed.