I know FF isn't like original works, and intellectual property can't be claimed (except in *some* very morally grey cases...), but the nerve of the request staggered me.
I don't think it's too uncommon for a fan or another author of fanfic to offer to "finish" or pick up a story you've dropped. I've seen it a few times. It's like one step past adopting a "plot bunny"! And it can be a fun way to collaborate, too. Don't be too offended by the request (and obviously, say no if you want), but it's not as "nervy" as you might think.
My current peeve is an author reusing the exact same trope, especially in the same series. I picked up several historical bodice-rippers for summer reading (about as far away from my usual stuff as you can get), and in every single one, the heroine ends up being kidnapped and sold into a Middle Eastern harem. It's a multi-generational story, so the initial heroine, two of her daughters, her brother's wife, and a granddaughter all end up as some raj/sultan/bey's treasured paramour and learn the exotic arts of love before returning home. Something tells me that if your family is that prone to being kidnapped into sexual servitude, you might consider staying away from ships.