The board shall have the power to examine into the facts upon which any pension shall heretofore have been granted under any prior or existing law, or shall hereafter be granted or obtained erroneously, fraudulently or illegally for any reason. The board is empowered to purge the pension rolls or correct the pension amount of any person heretofore granted a pension under prior or existing law or any person hereafter granted a pension under this article if the same is found to be erroneous, fraudulent or illegal for any reason; and to reclassify any person who has heretofore under any prior or existing law been or who shall hereafter under this article be erroneously, improperly or illegally classified. Any overpayments or underpayments shall be corrected and paid or repaid in a reasonable manner determined by the board.