If any surety on any such official bond should die or depart permanently from the State or if such board or the Governor, respectively, should, at the time of the annual examination or at any other time, be of opinion that any of the sureties is not worth as much clear of debt as his proportion of the obligation to which his name is affixed, the board or the Governor, as the case may be, shall cause the public officer whose surety has departed this life or removed from the State or is objected to for insufficiency of estate to be notified of such exception. Any such officer shall, within thirty days after the service of such notification, procure other surety satisfactory to the board or the Governor, as the case may be, but so as not to cancel or at all impair the original bond or produce satisfactory evidence to the board or the Governor, as the case may be, that the surety objected to as owning insufficient property, as aforesaid, is worth as much as his proportion of the obligation, clear of debt; or else the officer shall procure such additional and sufficient surety or sureties as the board or the Governor, respectively, shall approve. And in default of compliance with either of such requirements within thirty days the office of the defaulting officer shall be regarded as vacant.