It's not in David Stirling. It's in
CORPORATIONS CODE
SECTION 5220 which states [emphasis added]:
(b) Unless the articles or bylaws otherwise provide, each
director, including a director elected to fill a vacancy, shall hold
office until the expiration of the term for which elected
and until a
successor has been elected and qualified, unless the director has
been removed from office.
It's a conditional statement. A Director is no longer a Director once the term has expired
and upon the election of their successor. If only the term expired, the Director still holds the office until a new Director has been elected.
If you think about it, this makes sense. The business of the Association still has to be done. If there were no directors, the business of calling a meeting, sending notices, etc. could not be accomplished.