Massachusetts General Laws Part I. Administration of the Government (Ch. 1-182) Ch. 54, § 16

If a warden, clerk or inspector is absent at the opening of the polls or subsequently on the day of election, or if the office is vacant, the deputy of such officer shall act for that election in his place. If the warden and deputy warden, clerk and deputy clerk, or an inspector and his deputy, shall be absent, the voters of the precinct on nomination and by hand vote shall fill the vacancy, and the officer so elected shall act during the remainder of the election; but otherwise no deputy officer shall act in an official capacity or be admitted to the space reserved for election officers while the polls are open or during the counting of the votes.

In cities where no deputy warden or deputy clerk is appointed, if a warden or clerk is absent at the opening of the polls or subsequently on the day of election, or if the office is vacant, the senior inspector of the same political party as such warden or clerk shall act as warden or clerk for that election, and the voters of the precinct, on nomination and by hand vote, shall fill the vacancy in the office of inspector.