If you received a Notice to File a Business Property Statement from the Assessor and your business is no longer in operation, you are still required to file the Business Property Statement. You should also include a note on the Business Property Statement indicating that the business has closed, so the Assessor does not continue to assess the property.
The governing document of the LLC is called an operating agreement, and it is within this document that the members lay out all important provisions, such as standards for LLC governance, ownership parameters, and rules around member changes (adding or removing members, or what happens in case of death or incapacity of a member). The operating agreement is an internal document and is an agreement amongst the members or owners, which means it is not recorded with the state.
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".