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.
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.
Where the equipment you use in your business was acquired as a gift, you may report your estimate of its current market value on the Business Property Statement (that is, what you think it would sell for in the open market place). Enter that estimated value in the most current year's cost line and add a note indicating that the entry is an estimate.