Expecting that you are incorporated, corporate laws will apply.
Per the
WASHINGTON NONPROFIT CORPORATION ACT, specifically
RCW 24.03.100, despite your term ending, you will remain a Director until someone is elected, appointed or you resign.
If there are no candidates and all but one resigns, that single individual may appoint whom they choose that meet any qualification requirements outlined in your governing documents (if any) to serve on the Board.
If there are no candidates and everyone truly wants to resign, prior to resigning you would petition the courts to appoint a receiver. Having never done that process, I can't comment on the specifics other than to suggest that the Board should contact their attorney for assistance.
NOTE: Receivers answer to the courts not the membership. The membership will pay the salary and expenses of the Receiver. Therefore, you should expect assessments to drastically increase.
As I understand it, the Receivers job would be to manage the Association until a Board can be elected from within the membership. This would include, with the courts permission, to increase assessments to properly fund Reserves, levy special assessments if needed to address maintenance issues, etc.
As many have said, it's a last resort effort.
I have gone through the issue of no volunteers willing to run. What I discovered was once the issue was fully explained to the members and that the cost would come from their wallets, volunteers finally stepped up. You may want to do the same. It is amazing how many volunteers will step forward once you explain the costs for not stepping forward will be coming from their wallet.
I've attached an article I ran in our newsletter at the time. Perhaps it will be helpful.
Also, here is a link to the thread I started at the time about the issue,
Subject: Seeking advice on how to handle this issue. Perhaps you can find something in that thread that may help.
Tim