Death is a natural process. All living things go through a life cycle. We live and we die. Some die earlier associated to diseases or accidents. Human society behavior tends to overvalue life. Death is usually not spoken of or taught most of the time. No matter your beliefs, either religious or personal, death will be the end your life on earth. If you have negative thoughts about illness and jump to the conclusion that individuals will die, then it is most likely your beliefs and personal experiences in this life have taken you to reach that thought. We form bonds and attachments to individuals we love and appreciate. We want them to be with us forever and the thought of losing them is frightening. We must train ourselves to let go of everything we fear to lose (like Yoda said). If these thoughts affect your overall functionality and quality of life, then therapy can be an option. Psychotherapy, especially cognitive behavioral therapy, helps improve thoughts and emotions associated to your beliefs.
Hope this helps.