If a person is living in a NH & pays their personal income every month to the NH (which basically is their social security check - $30 they get to keep) & they die during that month, social security will want that $$ back so they would go after the NH since that’s who it was paid to, right?
Is the NH the payee for the SS check? If so, they are responsible to see that SS gets a check back that they are not entitled to. Now, if a family member is handing over the check each month, that person is responsible to make sure the money goes back to SS. Usually if direct deposit, SS takes it back the same way.
To answer you, the check received in April will go against the persons care for April. If they die this month, the NH has received the payment for the month of care.