The answer depends on which state you live in. The basis of property you inherit is usually the fair market value at the date of the decedent's death. If you live in a community property state, the basis for the entire property becomes the fair market value at the date of death. You simply quit filing a Schedule C with your income tax return. I went out of business this year and still have inventory on hand.
Inventory has to be run through the business when sold even after the business closes.
When an individual has expenses after the business has closed, they are still able to deduct these expenses.