Do not argue or try to change their thinking. It will not work, but only make them feel you are against them. Accept their reality as truth, for them and distract them to other things and get on with loving and living. They can die from a number of diferent causes. Pnemonia is common, sometimes persistent infections can lead to death and then there's those in the final stage that just stop eating.
Death is as individual to the patient as the disease was.
Most Alzheimers patients die of Alzheimers, as the brain gradually shuts down and then the other body functions just stop. If, of course some accident or serious complication occurs then death might be due to the complication. Yes, it could be, but it also could be a number of other things that only a very thorough set of exams and tests can determine. If she is aware and concened use the oppurtunity to suggest a visit to her doctors and accompany her. If not, it's up to you to figure out a way to get her to her doctor to facilitate the transfer to the correct professionals.