How do people die from Alzheimer's?

I believe the body starts to shut down as the brain isn't working correctly.

One example is that some patients forget how to eat and how to swallow, thus they stop eating/drinking, thus aspiration pneumonia could set in. Another example is falling because the patient forgets how to stand or walk and they have a very serious fall with head trauma. Another example is that the organs start to shut down and there is no way to reverse that.