That's not quite true either. State protection is neither necessary nor sufficient to consistently ensure safety for any particular person or their property. Obviously, there's a sweet spot.
Um, not that I know of. There probably are some, but very small. Depends on what you mean by area. When I spoke of "not necessary or sufficient", I thought I was careful to quantify that expression over individuals; sharing your original framing "no man's […]". Certainly some people may possess sufficient skill and will and influence and have few enough enemies to be safe for life without a state. And certainly some people possess such great weakness and incompetence and antipathy and have enough enemies that no state could protect them.
Maybe that's a nitpick on your phrasing but I am a licensed Picker of Nits (one who happens to be a minarchist, not an anarchist, for what it's worth.)