I know of a few companies that are able to write life insurance for people with Alzheimer's. Generally the policy amount is limited to less than $25,000 and it may have a reduced benefit should death occur due to illness in the first 1-3 years.

A related question- My mom with ALZ qualified for medicaid 3 months ago and she is in a nursing home. What happens to her life insurance when she passes? It's not a huge policy, but does it go to the state, the NH or to her survivors?