Who in the Potterverse manages to do magic only quite late in life?

Question

Q: Will there be, or have there been, any “late blooming” students in the school who come into their magic potential as adults, rather than as children? By the way, I loved meeting you, and hearing you speak, when you came to Anderson's in Naperville. I can hardly wait until you tour again.

JKR: Ahhh! I loved the event at Anderson’s. It was one of my favorites. That is completely true. No, is the answer. In my books, magic almost always shows itself in a person before age 11; however, there is a character who does manage in desperate circumstances to do magic quite late in life, but that is very rare in the world I am writing about.

(src: Barnes and Noble interview with J.K.Rowling, March 19, 1999)

Who was JKR referring to in “there is a character”?

Clearly, it not a student; so the most obvious guess of "Neville Longbottom" is wrong – both due to “no” answer regarding the question itself, and the fact that Neville bloomed in his 6th/7th year, well before you can legitimately term “quite late in life”.

Answer 1

Per Slytherincess' comment, JK Rowling had intended to introduce a muggle/squib character in the last novel that would somehow learn to do magic but then simply decided to take the story in a different direction and never wrote about this individual (e.g after she'd given the interview above);

Interviewer: You promised that someone will do magic late in life in book 7. I’ve now read it three times but can't work out who it might have been! Please help!!

J.K. Rowling: I’m sorry about this, but I changed my mind! My very earliest plan for the story involved somebody managing to get to Hogwarts when they had never done magic before, but I had changed my mind by the time I’d written the third book.