We do not know what the last star in the universe will be like exactly. But the one thing we do know is that, most likely at a certain point in the future there is going to exist a time where only one star is left in this universe. The reason that this would happen is because the most likely scenario which would take place is called the Big Freeze or Heat Death of the universe.
The current evidence of an ever expanding universe points out that, over a time as galaxies spread further away from each other, there will come a time where even the smallest particles will be getting further away from each other just like the galaxies are doing now. It will get to the point at which the temperature in the universe would be nearly absolute zero which is why it is called the Big Freeze.
Of course for such a thing to get to that point, first all of the galaxies will need to be spread out from each other. After that as the gas needed to form stars drains out, the star formation would stop leaving only select number of stars which will over a time go through their phases and eventually die out. Approximately stars could form from this point now to 1 trillion- 100 trillion years into the future. After that likely no stars would form.
So when all the gas that is needed to form stars is used up, that is when suddenly those lonely bright galaxies that are really far away will suddenly start to lose their appearance by dimming out over time as stars begin to die out. Once the stars stop forming in the universe, the stars that are already existing will stay there and they will stay there for a long time. After certain types of stars reach the white dwarf phase which is the last and longest lasting phase, they could be producing light for quadrillion years after which they will turn into theoretical black dwarfs.
When the stars die out in the far far future, eventually in the whole universe there is going to come a time when there is only one star left. What could also be the case is that there is not just one star but two stars orbiting each other or maybe even three in which case what is most likely to happen is that one star will become a black dwarf while the other one will be becoming as well but it will still produce some light. So there will be a black dwarf and a white dwarf orbiting each other.
As of now in our galaxy alone there are hundreds of billions of stars and in universe there are 2 trillion galaxies. This means that there are around 200 sixtillion stars as of right now. So despite these many stars, there will come a time where there is only one star shining. We have no idea for how long this last star could go on but there will also come a time when it also becomes a black dwarf and dies out. During that event, those will be the last photons that will ever get released after which the big freeze would occur and there will be no light left in the whole universe.