§ 57. Terms of elective county officials not to be abridged. The term of office of an elective county official shall not be abridged by reason of the approval of any question providing for the adoption in the first instance of an alternative form of county government or modification, change or abandonment, of any such form previously adopted. If an elective official of the county is continued in office after his office is abolished, he shall perform such related duties for the remainder of his term, unless a vacancy otherwise occurs, as may be assigned to him: (1) in case of the modification or change of an existing form of county government, by the county executive; or (2) in case of the abandonment of an existing form, by the board of supervisors of the county. He shall be paid a compensation to be fixed by the board of supervisors and paid by the county.