The process of moving a person with dementia to a care home is one that's often left to the family or the person who has durable power of attorney (DPOA).
If an older adult with cognitive impairment has neither family nor a DPOA, the state would step in and appoint a guardian to make decisions about care.
Regardless, of who makes the care decisions, the nature of dementia which you point out, requires an increase in the need for assistance over time. If that need significantly exceeds what can be managed safely at home on one's own, home care is often the first intervention. If the person has limited assets to pay for home care, a nursing home is often the next step as the cost of a nursing home can be covered by Medicaid for those who qualify.
Those with dementia (and without)and substantial assets have additional options. They can pay for additional care at home - as much as needed - or they can move to an assisted living facility that has a special floor for those with memory impairment and pay for 1:1 care there as needed. The third option for this group is what I think you are alluding to when you talk about an owner-occupied residence where meals and care are all included...this is commonly known as a "Board and Care facility".
Most often, Board and Care facilities are free-standing homes within the community that are operated like mini-nursing homes in a way. The monthly fee which is not to my knowledge covered by Medicaid, includes room, board and care, hence the name. A Board and Care can be an excellent setting for receiving highly personalized care however, they don't exist in all states.
I hope this helps.