This is a short story, which I'm pretty sure I read online. The narrator was sentenced to life in prison, but after sentencing, some sort of nanotechnology was released, infecting everyone and making them immortal.
The narrator (male) is now hundreds (thousands?) of years into a life sentence, and feels like he has been forgotten by the rest of the world.
Note: I saw this similar question, but neither of the stories proposed on Looking for a short story about a society where when you are sentenced to life in prison, you are kept alive in prison forever is what I am looking for.