If a person is 65 and older and has medicaid then Medicare will cover up to 100 day of skilled nursing home care but under limited circumstances when it's needed medically.
So yes if the person has dementia then they'll likely be covered for and have the skilled nursing care in a nursing home paid for by medicaid for at least 100 days.
Then after 100 days you'll need to check with other insurance or have the patients assets pay for the nursing home care after the 100 days is up and the dementia patient still needs nursing home care.