Others have linked some relevant articles, but I think the one that most directly addresses your question is Belief in the Implied Invisible. (I tried to expand it in the context of Tree Falls in a Forest ...)

Long story short, in order to have a model that says the person stops existing when unobserved, you immensely complicate your description of the world, because you would have to throw out all kinds of regularities you rely on, like conservation of mass.

You can certainly get away with simply positing the concept of "my reality" like your friend does, and say someone stops existing in that sense, but it's unclear what would be the point of doing so, since the concept is (as far as I can tell) precisely identical to "I don't detect that person", so you already have an expression for it.