Remember that matter and energy are equivalent (E=MC^2), and that matter/energy is a conserved quantity in our universe. Therefore, matter/energy will not "die" out. Latest observations indicate that the expansion rate of the universe is increasing, and if true, it means that matter/energy will be increasing diluted over ever increasing volumes of space. The energy density of the universe will appoach zero, but the total quantity over all of space will remain the same.
-
Everything dies eventually.. There is nothing in this world, and beyond that lives infinitely. So yes.