Are far-away galaxies light years distant still there?

Galaxies, of course, are not the same as individual stars. The Milky Way galaxy, for example, contains 200 billion stars and is about 150 000 light years across. This means that a star on the opposite side of the Milky Way from our own solar system has been travelling for 150 000 years before it arrives at the Earth. The next nearest galaxy to our own is the Andromeda galaxy and that's about 3 million light years away, so the light that's coming from there is already 3 million years old. So it's beneficial that some suns are very long lived - suns like our sun live for 10 billion years - so there's more than enough time for light to come from the Andromeda galaxy. But you've asked a good question because space is so vast that inevitably light that's coming to us from stars up there in the sky will actually be signs of a star that's died. One day those stars will wink out because they don't exist any more, but at the moment the light is still coming to us because there's a bit of a delay. So there will inevitably be some stars but I doubt there will be a whole galaxy because they contain billions of stars and they'll all be at different phases of their lifetime.