There are three things I can imagine happening:
- It appears one light year further away every year, which would be a bit weird, because it would be behind the universal event horizon, but still visible. It would appear completely unaffected by the Big Rip (which might be understandable, because it's in the past). And in the far future you would only see Milkdromeda, then a loooooooooot of nothing and then the cosmic background radiation. Also, what would prevent you from seeing things that happened shortly after the universe became transparent?
- It disappears behind the universal event horizon, which would be weird, because it was everywhere. Could there be anything preventing the photons emitted back then from reaching far future observers?
- It appears to get closer, matching the seemingly shrinking universe (from universe to galaxy to solar system…). This variant might appear the least weird to far future observers ("That's just how big the universe is, there is nothing beyond it."), but I see no reason why it should appear to shrink.
Is it any of these? And why?