My approach is that the “person” itself is just ideas that live in people’s minds, and isn’t an actual physical thing. So much of what people think of when they think about a person is views, moral standings, social standings etc of the person, all which don’t actually exist as physical objects. Which is demonstrated by the fact that people don’t use “Kissinger” to refer to his ashes or whatever.
Edit: Which kind of means that the person does live on in the minds of others, just like the cliché goes. But it isn’t “real” anymore because it doesn’t associate to a physical object anymore.