The law specifies that all taxable personal property must be assessed as of a specific point in time, and that point is precisely at 12:01 a.m. January 1 (regardless of what transpires after that date). Even if closed shortly after the lien date, a business must still file a Business Property Statement and pay taxes for the coming fiscal year on any taxable property they owned on the lien date.
Outside of the normal statement filing season, you may fill out a Statement of Change form with the date you went out of business, the status and disposition of any equipment owned or used by you at the time the business closed. If any of the property was sold to another person or business, please indicate the buyer's name and address. Make sure to identify any property that reverted to your own personal use as household personal property.
A grocery store goes out of business prior to January 1st but equipment such as freezer boxes and store shelving remains in the building on that date. In this case, such items would still be taxable and must be reported even though the business was closed on the Lien Date. That is because in this case, the equipment could not revert to or be used as "Household Furnishings or Personal Effects".