If any county detective, after having been retired on one-half pay, shall die, or having made application for retirement, shall die pending the completion of his papers and action thereon by the board of chosen freeholders, leaving him surviving a widow, who was his wife at the time of his retirement, or application for retirement, such widow, so long as she shall remain unmarried, shall receive a pension equal to one-half the amount of the annual salary of such county detective at the time of his retirement, or in case of his death before said action by the board of chosen freeholders, then at the time of his death; provided, however, that before his death he shall have been examined by the board of physicians and their certificates shall have been made in accordance with the provisions of sections 43:10-23 and 43:10-24 of this title finding him physically unfit or incapacitated for further duty.