What does a spouse do when death occurs and that spouse had a home in their name only through inheritance and a car ?

If there is no will, the surviving spouse will have to apply to court for the statutory share guaranteed to the surviving spouse.  It is not possible to disinherit a spouse, therefore every state has adopted regulations and statutes that establish the minimum share that the surviving spouse is entitled to receive.  This share is typically 1/3 with remaining shares going to the children and/or parents.