R.I. Gen. Laws § 7-1.2-804: Vacancies.

Any vacancy occurring in the board of directors may be filled by the affirmative vote of a majority of the remaining directors though less than a quorum of the board of directors. A director elected to fill a vacancy is elected for the unexpired term of his or her predecessor in office. Any directorship to be filled by reason of an increase in the number of directors may be filled by the board of directors for a term of office continuing only until the next election of directors by the shareholders. If at any time, by reason of death, resignation or other cause, a corporation should have no directors in office, then any officer or any shareholder or an executor, administrator, trustee or guardian of a shareholder, or other fiduciary entrusted with like responsibility for the person or estate of a shareholder, may call a special meeting of shareholders in accordance with the provisions of the articles of incorporation or the bylaws, or may apply to the superior court for a decree summarily ordering a meeting for the purposes of conducting an election.