Where is the Federal government getting the money to give to States for programs like this (and many others)?
From people paying taxes ... people living in States, or borrowed money that will eventually have to be paid back by people living in States.
So 100% of the money is coming from the States. The States are not getting any free money from the Federal government. They are getting their own money back.
The government wants the oldsters’ property. Getting them on Medicaid gits ‘er done.