1.) You're a paramedic in the U.K. (North Cornwall, specifically, but that's not too important) and you've been called to a house out on the cliffs where one of the residents has reported finding a young woman naked on the beach and unconscious. When you get to the house, you find that the caller has put the woman on a sofa, piled her with warm blankets and lit the fire.
What's the procedure? What do you do? I assume check for hypothermia, but how and what does that involve?
2.) Now you're a doctor/social worker/policeman, whoever would be involved in this. The young woman in question is taken to hospital but is found to be in good physical condition, though exhausted and obviously in shock, with no injuries and no hypothermia. As she recovers, it's discovered that she can't speak, and is suffering from total amnesia - she doesn't know her own name, she doesn't know anything about where she is or what has happened to her, and she can't read or write.
There are no reports of missing persons. There's absolutely nothing to link her to anyone or anything. She shows no signs of being mentally ill or below average intelligence (although obviously it's hard to tell without written or comprehension tests) - as she recovers she shows a lively, adult interest in the world, she's keen to learn to read and write, and quick to pick up sign language.
She is very, very insistent that she wants to go home with the people who found her. They are willing to take her in.
Again, procedure? Legalities? There's no reason to keep her in a hospital. She is at least twenty, so she's not a minor. Is there anything to stop her walking out? She has a place to stay, she is clearly an adult. Do you let her go? Does she have to be entered into society, given a name and a national insurance number? Who has the final say, or does anyone have any say in it at all apart from her?