If you want to see what the authoritative figures have to say on the topic, here's a quote from What Happens to an Arahant at Death? A Dialogue between Bhikkhu Bodhi and B. Alan Wallace:
BB: The problem then is how nibbāna after the death of the arahant can be a real element (a real entity, a real dimension, a real state, whatever term one uses) describable as “ultimate bliss” etc. yet without being identifiable with viññāṇa. [...] I take such terms as “unborn, deathless, etc.” to be referential, not mere metaphors for absolute extinction. The problem is how to bring together this ultimate reality of nibbāna, conceived as a state that (even post-mortem) is “peaceful, blissful, auspicious,” etc., with the denial that consciousness or mind is present. It’s a problem I haven’t been able to solve.
If you want to know my opinion, here it goes:
"By & large, Kaccayana, this world lives by duality, that between existence & non-existence. [...] Avoiding these two extremes, the Tathagata teaches the Dhamma via the middle.
What does this mean? When we say something exists, we assume that something is a distinct object that goes through time. We say, in some way it changes but in some ways it stays essentially the same. And then when it falls apart we assume that essence is irretrievably gone. But in reality that's a huge simplification, rather like the mythical geocentric model that people have learned to carry on without questioning. The geocentric model used to posit existence of "celestial sphere" to which the stars are attached, because that's how it looks indeed.
Entities are abstractions, simplifications. Not just sentient beings, but even relatively static objects like chairs are cross-sections of multiple streams, if you trace their lifecycle and the lifecycles of their parts. And when chairs are not used as chairs they are strictly speaking not even chairs, they are just oddly shaped stuff. Things exit in a certain way only in relation to processes they participate in.
So entities are a simplified way to talk about what really is a bunch of dynamic processes and many, many nested contexts. Matter, energy, and information are always in flux, on many levels.
When we say Andrei, there's this rice and milk, there are these books, these questions, these squirrels and birds, this heat, this job, these people, this country - and tomorrow these will continue in similar combinations. Andrei is not something static and concrete. It has never been something static and concrete. Because it's not something static and concrete, the labels like existing and not existing do not apply. Since labels like that do not apply, birth and death do not apply.
Mind is not "inside". My awareness is not mine. You asked a question - it became my thoughts for a day. Now as you are reading this answer, my thoughts are your thoughts. Then you'll read a tweet, then you will watch a movie, then you will hear some news about Trump. Get it? Our thoughts come from the environment, our memories come from the environment, our feelings come from the environment, our choices come from the environment, our bodies come from the environment. There is nothing you can pinpoint and say "this is an arhat". Or I guess you can of course, but doing that is exactly the framework that leads to suffering. And when you stop pinpointing you see that in fact it has always been rather loose. Then you transcend the framework that operates in terms of "entities", "exists" and "death" and by doing that un-base all passion, aversion, confusion, and suffering associated with that. That's what's called "an arhat".
Because mind is not "inside" (and life in general is not inside) - it will go on "like a rolling stream", just not always going through this particular scull. Hopefully one day, with all the efforts put in making Buddhism mainstream, the bad habit of reifying entities and identifying with them will be outgrown.