All personal representatives and conservators, who by the establishment of a new county, or the alteration of county lines, shall cease to be inhabitants of the county in which they were appointed or received their letters, shall nevertheless continue to render their accounts and make settlements, and in all things proceed in the courts by which they were appointed, or their accounts remain to be settled, in all respects, and be subject to the like proceedings therein, as if such new county had not been established, or such alteration had not been made.