The idea is a young woman whoi gets one wish granted each year on her birthday.
The catches are:
1. She has no control over this. Her first conscious desire after the clock strikes midnight on her birthday counts as the wish, even if it's something as simple as "I'm hungry".
2. She is unaware of the phenomenon, as most of her "wishes" were pretty simple and she never drew the connection. For example, in the case of the "I'm hungry" wish, it would be fulfilled by her sense of hunger suddenly abating for several hours which she might consider odd, but not mysterious, and would probably forget about by the next day.
Containment procedures are standard for humanoid SCPs (kept in locked room, fed, given a few basic amenities… going with the standard "prison" setup) except that on the day before her birthday each year, she is to be administered a powerful sedative which will keep her unconscious until the day after her birthday.
She was discovered by the Foundation after observing a pattern of anomalous effects occurring on the same day in three separate years, two in the same town and one in another town, they found her by researching to discover that her birthday was on that date, and she had lived in both towns on the day those things took place. One of the anomalous events would be a thunderstorm suddenly dissipating with no meteorological explanation, due to a wish for it to stop raining. (Of course this would be covered up by the Foundation and presented in the media as just the storm ending naturally). I haven't come up with the other two yet.
Among the belongings of the girl's family would be a hand-made birthday card given to her on her first birthday, with the message "May all your birthday wishes come true! Love, Aunt Sarah". Investigation would find no evidence of the existence of this Aunt Sarah.