People grieve by feeling and expressing many emotions, even some that are conflicting. Sadness is an emotion that comes immediately to mind, but anger is also common. People may feel angry at God, at the doctors, and at the person for dying. These feelings may not seem rational, but emotions by their very nature are not rational. All emotions are normal and to be expected.
It is also common to feel relief after a loved one dies, and then to feel guilty. If the person has suffered, it's easy to feel relieved that he or she is no longer in pain. But feeling relief for yourself is perfectly natural as well. Whether you have been a primary caregiver or not, a terminal illness is likely to have disrupted your life and may have caused tension as you juggled and rescheduled your ongoing responsibilities. Or, you may inherit money from the deceased, which can help relieve stress and result in an easier lifestyle for you. It's not your fault that you benefited from the death.