Nothing can't exist. There always has to be something even if it's not You. This doesn't mean that You'll have an afterlife in heaven, necessarily, but that someone or something else will exist when You (right now) are dead/forgotten and that someone or something will experience existence the same way You are right now. It's not that you're connected directly to them, but your death is a non-experience to all living things. The same way You're here right now while other people you'll never know, while people who have died, while people who are being born have no effect on your life. You already don't exist to some people, instantly and eternally. They don't perceive your existence and won't perceive your non-existence. When you stop existing, the others who exist will have the same relationship with you that you have with people who are already dead now. Instantly.
Very hard to put my perspective into words, maybe someone else can clarify.
I'm not saying there'll be reincarnation of you as is. It's just that non-existence can't be. Your identity dies but the experience of being a human being continues in others. Not even sequentially (as in you have to die first, then someone is born the instant you die). Existing and living is all that can be known.