nokidshere at the privileged/ poor little rich girls (although they seemed fine, not unhappy) end of the scale I had a both a friend and an acquaintance at boarding school, both of whom left at 16 and then lived alone.
One had parents living in a troubled middle Eastern country who owned several properties in the UK and gave/ lent her a flat to live in while she attended an FE college, having not done well enough for A levels, and worked part time. They thought it would be good for her apparently. It was I guess. She had two older half siblings at university in the same city, living in different areas of the city, as emergency contacts but didn't see them much. She eventually made it to university herself. She wasn't truly independent (certainly financially as she had no rent to pay) but she definitely lived alone. I visited her for long weekends almost every holiday while I was at 6th form telling my parents her sister lived in the same flat, which wasn't true
My acquaintance was in a different school year but her mum had died much earlier, when she was very small, and when she was 16 her dad sold his business, gave each of his children their inheritance and fucked off to live on a yacht and "cruise". She was the youngest and bought a cottage in a pretty village beloved of retired people, slightly oddly. She dropped out of school for a while, then later did secretarial qualifications, later she started working. She lived alone - though her financial independence was due to the privilege of having been given a very substantial sum which she lived on for quite a while. She got married in her 20s but she definitely lived alone from age 16. She had family friends in the area and older siblings scattered throughout the country, but nobody specifically "looking after" her.
I think only the very wealthy and the very poor/ underprivileged usually live alone at 16. It's not an "ordinary" experience but it happens.
Even now a colleague's daughter lives in a rented room with an elderly couple several hundred miles from her parents because she wanted to do a specific apprenticeship not widely available and has a place in a city at the other end of the country. My colleague got her settled there, checked everything out etc but and is on the find of the phone. The couple aren't in charge of her and weren't part of any specific arrangement for the apprenticeship, they were just looking for a lodger. Her daughter is 18 now but was 16, nearly 17 when she moved. She's also living alone to most intents and purposes - at least not with a carer or parent.