How can I find help for a brother who is jobless, homeless and is mentally and medically ill? Looking for shelter and income.

Someone will have to seek guardianship. It is unlikely to be won if the brother doesn't want it. If he will not be diagnosed incompetent in his own behalf and give guardianship to family member there is quite honestly little you can do, and that is but one of the reasons you see some of the homeless and incompetent in the streets. Have you spoken to the brother, and what is his response to you?

I'm assuming you are not his legal guardian... when you say "he will need to leave soon" I'm wondering if this is you wanting him to leave -- if so then fyi: if your mom's home has been his only residence for a while, and he doesn't want to leave, it may be challenging to get him out (as in eviction process). To find housing options for him, SSDI and Medicaid help, contact his county's social services at the Dept of Health and Human Resources.