The stars in Freelancer have damage numbers. Say one sun can be set to do 5,000 damage. Then another one (usually bigger or brighter ones) can have 100,000 damage. The thing about being killed before you reach the center is affected by both damage and the extent of the sun corona. A sun with a corona stretching 20K with a damage of 5,000 could kill you farthur away from the center than a sun that extends 5K and does 15,000 damage. Also the distance into the corona you are determines what factor of the damage you recieve. So a star that does 100,000 damage will do 100,000 damage if you are sitting within 2K of the center. But if you were sitting say 10K away you are likely to get about 10-20k damage.
Also Stars damage are not affected by armor upgrades. They take the damage directly from you hull points.