Will the universe come to an end one day and die out like the stars? Or, will the universe go on forever?
No one knows.
This universe is expanding and doing so at an increasing rate. Present theory says all galaxies are moving away from every other galaxy.
Right now we believe the universe will continue to expand until one of two conditions happens: all the stars in all the galaxies burn out, or, the universe almost literally tears itself apart. That is, as everything in all the galaxies continue to accelerate, at some point they will right the speed of light and rip apart the very subnuclear particles.
There is also still some belief that the universe will at some point reach a maximum acceleration because gravity associated with dark matter will take over and at that point the universe will start contracting.
Everyone is guessing, but no one knows.