Wealthy people are eligible for Social Security, as long as they did not accumulate their wealth through passive means, according to The Motley Fool in "Do Billionaire's Get Social Security?"
If a person worked at least 10 years and paid into Social Security, they are eligible no matter how much money they have.
Whether wealthy people should get Social Security or if the program should be limited only to those without the means to take care of themselves, was a subject of debate at the time the program was founded.
President Franklin D. Roosevelt ultimately decided that the program should not be means-tested, so it would be viewed as a universal right by people. He believed that would make the program much more difficult to cut or eliminate, if future politicians tried to do so.
Later events seem to have proven Roosevelt right about that.
Politicians have found it difficult to make cuts to Social Security.