With the proper planning, limited liability companies can exist for generations. S-Corps continue to exist even if the owners or majority shareholders leave or pass away. C-Corps continue to exist even if the owners or majority shareholders leave or pass away. Non-Profit organizations and institutions survive after their directors leave. Sole Proprietorships do not exist when the owner quits or passes away.
On the other hand, if you are not responsible for its tax, then you should declare the equipment in Part III of the Business Property Statement (Equipment belonging to others). Where equipment is declared in Part III of the Business Property Statement, the Assessor will also send a Notice to File to the person reported as the equipment's actual owner.