Legal Question in Business Law in California

Probably. First of all, a "closed business" can be one of many things. It can be that a healthy corporation shut down a single store, or maybe a whole chain of stores. It could also be that a single entrepreneur shut down after dying, or after filing bankruptcy. There's a whole bunch of other possibilities, each with different consequences as to who may be sued, liability to former customers (or employees, etc.), and so forth.

Typically, but certainly not the only situation, is where a business is run as a corporation. The corporate law expects that when a corporation ceases to operate, it will shut down its activities in a fair and logical sequence -- collect its receivables, liquidate its fixed assets, pay all its liabilities (including making a provision for contingent liabilities such as lawsuits), and then and only then return whatever's left over to its stockholders.

There are somewhat parallel expectations when other forms of businesses close - a business cannot simply return all its assets to its owner(s) and let its creditors hang out to dry. Even in a bankruptcy, the court will try to spread out available assets to various classes of creditors according to a formula set down in the Bankruptcy Act.

In general, you should name as defendants, and serve, all potentially-liable parties, including the business itself, and probably its identifiable owners and managers. However, such a shotgun approach is not advisable when you have some reliable information about the status and structure of the business, the roles of its owners or former owners, the depth of the remaining pockets, and other info.