An insurer of a suspended corporation has an incentive to defend the corporation because it may be liable to a judgment creditor that obtains a default judgment against the insured suspended corporate. See Cal. Ins. Code § 11580(b)(2).  However, can the insurer defend a corporation that is suspended?  The Ninth Circuit Court of Appeals recently held that California law permits an insurer to intervene in its own name to defend an insured suspended corporate.  Travelers Prop. Cas. Co. of Am. v. Liberty Surplus Ins. Corp., 2020 U.S. App. LEXIS 7847.  

Suspension may occur under Revenue & Taxation Code Section 23301 and/or Corporations Code Section 2205  As to the former, the Court of Appeals noted that while California law imposes criminal liability on "any person who attempts or purports to exercise the powers, rights, and privileges of a corporation that has been suspended pursuant to Section 23301", the statute expressly says that "nothing in this section shall create or limit any obligation upon an insurer to defend a suspended corporation."  See Insurance And The Suspended Corporation.  As to the latter, the Court could find no case that expressly prohibits an insurance company from intervening in a lawsuit to protect an insured suspended under Cal. Corp. Code § 2205. 

The case is unpublished and is not precedent except as provided by Ninth Circuit Rule 36-3.