(a) Upon motion by any party or representative or upon the Board's own motion, an appeal may be dismissed upon its abandonment by the party or parties who filed the appeal. Within the discretion of the Board, a party may be deemed to have abandoned an appeal if neither the party nor his representative participates significantly in the review proceedings.

(b) An appeal may be dismissed on the death of a party only if the record affirmatively shows that there is no person who wishes to continue the action and whose rights may be prejudiced by dismissal.