Father died in a nursing home and he had funds left in his account with the home. Is it true that they can only send money to funeral home?

Alva is correct. The Nursing home is wrong. Look up personal needs

If there is an executor, they can go to the probate office and for a fee get a "short certificate" which gives them the ability to handle what is left in the estate. They take that certificate to the NH. For me the money was offsight so the info was sent to them. A couple of weeks later I received the check. It does not go back to Medicaid. If they argue the point tell them to show u were it says it goes towards funeral expenses.

If no will then someone can still go to probate, become an Administrator and get the "short certificate".

The money is your fathers. SS allows it to be put aside.

On Medicaid there are specific rules about money left after death. Unless the account is set up as joint or transfer on death, the money goes to estate for probate. In probate Medicaid gets first dibs on accounts with leftovers. If you have a bill to pay directly to funeral home that can sometimes supersede. Your name would indicate Medicaid is in the picture.

The money is part of his estate. This now goes to whomever is executor and a filing of probate. The executor should understand that this money is there and should be collected into the estate. The estate will them pay what Granddad has to what bills he has, leftovers to the heirs.