If death (assuming no afterlife) erases your conciousness, it should also erase your memory of ever having been concious. It should be as though you never existed at all, right? Not just future and present gone, but past.
So then how are we here, being concious and remembering stuff? How could that be unless the universe is inherently static, or at least endlessly self-repeating, and us being concious is just a permanent feature of our corner of it?
Has anyone else thought about this or am I just rambling?
You should take a closer look at what "memory" is as it relates to consciousness. I'd argue that for a consciousness experiencing a memory is the same transient experience as any other qualia like hot, red or pain. Hell, you can imagine a conscious being that doesn't have (subjective experience of) memory the same way as you can imagine a conscious being that has never experienced "red".
Also another interesting way to recontextualize those kind of questions is to ask them not about meat-and-bone people but about computer simulation people a-la Black Mirror. Do they have consciousness? Do they have memory? Can they die? What would happen to memory then?