Wow. Some people know no bounds, Crochet. You might want to put up something in your profile that all stories are yours, to not complete them, and put a complete tag on the ones that are complete.
I'm considering that, but I don't want this person to think I'm singling them out (not the SSW, but the one who messaged me last night). This person left a signed review also asking the same question, and last time I checked those can't be removed. I tend to give people a bit of a pass on a nervy request if they accept my "no" graciously and move on. Now I'm on pins and needles worrying about seeing a continuation of my story by some other person who didn't bother to ask permission. Well, not really...I'm not super worried about it, just mildly irked. If someone else asks me, though, I'll definitely put a note in my profile.
Maybe put in your summary that you are indeed planning on completing the story and you aren't going to have anyone else complete it for you and anyone else doing so will be reported.
As for the other person who was asked, tell her/him that if your story inspired them into writing, to go for it. But remind them to make sure they tweak their story enough so that it is not part of your particular branch of whatever fanfic universe you're writing in.
In my In Progress files, I have one like that. I got to thinking, what if this happened instead of that. A main character was depressed because he lost his girlfriend and because he wasn't paying attention to what was going on around him, he got kidnapped. As the origional author had added several new characters to his/her story, I knew that I couldn't use those characters, even changing their names would be a no no, so I tweaked it out of that author's version of how they felt the show could have gone, did my own thing with it. Instead of the character being depressed and not paying attention and getting kidnapped, he was excited and not paying attention and getting kidnapped. No need for the other author's characters at all.
I hope this SS fan finally gets a clue, quits pestering you about your story, and starts spending her time writing her own stories.