Mass. Gen. Laws ch. 43A § 9
Any vacancy in the full number of town meeting members from any precinct, whether arising from a failure of the registered voters thereof to elect, or from any other cause, may be filled, until the next annual election, by the remaining members of the precinct from among the registered voters thereof. Upon petition therefor, signed by not less than ten town meeting members from the precinct, notice of any vacancy shall promptly be given by the town clerk to the remaining members from the precinct in which the vacancy or vacancies exist, and he shall call a special meeting of such members for the purpose of filling such vacancy or vacancies. He shall cause to be mailed to every such member, not less than five days before the time set for the meeting, a notice specifying the object, time and place of the meeting. At the said meeting a majority of the members from such precinct shall constitute a quorum, and they shall elect from their own number a chairman and a clerk. The choice to fill any vacancy shall be by ballot, and a majority of the votes cast shall be required for a choice. The chairman and clerk shall count the ballots and shall make a certificate of the choice and forthwith file the same with the town clerk, together with a written acceptance by the member or members so chosen, who shall thereupon be deemed elected and qualified as a town meeting member or members, subject to the right of all the town meeting members to judge of the election and qualifications of the members as set forth in section five.
Mass. Gen. Laws ch. 43A, § 9