Maybe this will help explain. I found it in the Atlanta-Journal Constitution:
How does Alzheimer’s lead to a person’s death?
Alzheimer’s disease destroys nerve connections in the brain, making it progressively more difficult to do ordinary things like move around, swallow and feed yourself. While the disease devastates the brain, it does not kill you. Complications of the decline in brain function is what leads to death. Not being able to swallow properly is particularly dangerous. The vast majority of those with Alzheimer’s die from aspiration pneumonia – when food or liquid go down the windpipe instead of the esophagus, causing damage or infection in the lungs that develops into pneumonia.