Until they are so far redshifted that they fade into background noise. And the expansion of the universe is accelerating. We have a bit time to watch this spectacle, but the fate seems it is just our local cluster that will matter, for most of the time while stars generate heat. That is why I am not so keen on emphasising the billions and billions of galaxies. It's only a nice good-bye firework.

Edit: I still think there are much more galaxies in our universe than stars in our milky way: The universe must be bigger than our observable part and there is no reason to believe that it is much different there (read less or no galaxies) than where we happen to be. So the "eternal redshift" already happened for many galaxies (from mutual perspective).