If the theoretical data is available on the theoretical abuser, the police could monitor it, or you could have a non-profit service which monitors the proximity and alerts authorities / sends a "get out of the house" message to you.

So, instead of living a life in relative safety, you get to spend the rest of your life on alert and in fear. I really don't see how you can argue that this would be an acceptable solution.

No I would have no problem if they just watch, only if they did something hurt then its problem. In open society they can be tracked easily.

Great for you, but I think that you understand that not everyone would feel the same in such a situation?

The most theoretical part of such a scenario is the police force that follows procedures perfectly and aren't ever overworked.