That's how feeder characters work, that's why i said yandere could be a feeder personality. What is suggested here, kidnapping and following you even to other towns, is too extreme - in the sense of game breaking.
I think it could work, but it would have to be an opt in/opt out feature like how you can disable getting called for dates and stuff, because I otherwise agree that the suggestion would make the yandere way too disruptive if you came across one via random generation.