The California General Corporation Law provides that any director may resign effective upon giving notice to certain specified persons, unless the notice specifies a later time for the effectiveness of his or her resignation.  Cal. Corp. § 305(d).   On its face, the statute requires no prior approvals for a resignation and imposes no limitations.  Cf. In re Puda Coal, Inc. Stockholders Litig., 2013 Del. Ch. LEXIS 338, *19-20 (suggesting that resignation may involve a breach of fiduciary duty).

The same is not true of California nonprofit mutual benefit corporations and religious corporations.  In the case of these corporations, no director may resign when the corporation would be left without a duly elected director or directors in charge of its affairs.  Cal. Corp. Code §§ 5226 & 9226.  In the case, of a mutual benefit corporation, the statute provides "except on notice to the Attorney General".  Thus the sole remaining director may resign if she gives notice to the Attorney General.  No such exception exists for religious corporations.  Thus, for directors of these corporations, there may truly be no exit.  

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