Immortality means you'll outlive the universe. ~150,000,000,000 years from now, when the heat death of the universe comes around you'll still be there, alone in space and time. Forever.
A more cheerful scenario is you fly too close to a neutron star and get caught in the gravity well. Splat! onto the surface of the star, and smashed down to one molecule, perhaps one atom, thick. But you're immortal. Still alive. Stuck there forever. Hopefully it won't hurt much. Hopefully.
A more cheerful scenario is you fly too close to a neutron star and get caught in the gravity well. Splat! onto the surface of the star, and smashed down to one molecule, perhaps one atom, thick. But you're immortal. Still alive. Stuck there forever. Hopefully it won't hurt much. Hopefully.