Section 111E. Whenever the employment of any person subject to section one hundred and eleven or sections one hundred and eleven A, one hundred and eleven D or one hundred and eleven G is terminated during a year by dismissal through no fault or delinquency on his part or by resignation, retirement or death, without his having been granted the vacation to which he is entitled under such section, he, or in case of his death, his estate, shall be paid, at the regular rate of compensation payable to him at the termination of his employment, an amount in lieu of such vacation; provided, that no monetary or other allowance has already been made therefor. The official head of the department in which the person was last employed shall enter on the departmental payroll all amounts payable under this section. The provisions of this section shall also apply to any person not subject to any of the aforesaid sections whose service is terminated as aforesaid without his having been granted the vacation to which he is entitled under a by-law, ordinance or executive order; provided, that such by-law, ordinance or executive order so provides.