Are there any private home facilities where only three or four elderly people live and receive care?

You can usually find these homes through your local dept of aging..Check with your llocal social services dept as well. Or you can go one the web and ask for Board n care etc.

Some states have "Board & Care Homes", these are as you described. Usually the maximum is 8 and is owner occupied and the residents can't have too many health care issues as the home is not licensed for nursing care.

All areas do not have the homes, since they are private initiatives usually. You would have to learn about them through the normal community routes -- advertisements, yellow pages, computer, word of mouth. I hope you can find one in your area.

This sounds good to me....sorta what I want, I think. How would I go about finding a place like that in a specific area?

Yes, there are people who have small businesses in houses. These residential homes are not care facilities, but are more like assisted living. People cook and clean for clients and help with medications. Typically there is a common room for TV and another for eating. This allows for socializing among the residents. However, the homes are not skilled nursing facilities, so do not handle healthcare matters. There are limits on how disabled clients can be to qualify to live there.

Adult Foster Care. Check to see if you have them in your area. In Oregon, it's an up and coming idea.