How do people who are too disabled to apply for disability get disability?

John Doe cases do happen from time to time. In that case they become wards of the state until they can be identified. Their photos are usually circulated in the area where they became lost and/or they are posted on listing person sites/news/milk cartons. They generally will live in a nursing home paid for with state dollars. A para who is deaf, blind, and intellectually disabled is very unlikely, but a person with Alzheimer's is not. A person who cannot sign their name can sign an X with a witness present that can sign their name and knows the person is who they say they are. A representative can apply for a person with a severe disability, not unlike parents who apply for their children.

well I guess the same way some one who is not disabled gets disability. ;p

Someone else would do that for them. In cases where people aren't capable themselves, a certain person will be nominated to handle those things for them