Most likely there will be no "you" to speak of after the fact, so it's sort of meaningless to think about what will happen to you. The last things you will experience will be the moments just before total brain death, but what happens in consciousness during those moments will depend on the person and type of death. There's no way to know for sure without going through it, but it's possible that time might slow down to the point of infinity, you might find eternal peace and bliss or you might go through some freaky multidimensional realms. You could also just get cut off.
Anything could happen really, but once you're gone, you're gone and will be gone for the rest of time in this instance of the universe. At the same time you will remain engraved in the fabric of spacetime forever as no information can ever truly be lost and time is not linear. You might dissolve into everything and become nothing, or the other way around, or both at once. I get so lost every time I try to comprehend it though, so here's a good quote I resonate with that's quite simple and does the job:
"The day of our death is the birth of eternity"
And eternity has two sides - ∞ and 0
You can go a bit crazy if you think about it too much, but one thing's for sure:
When we die we transcend spacetime and go back to the singularity of infinite possibility