The institution of the Twelve Apostles was meant to last forever. The individual Apostles would have died, and others would have been appointed to succeed them.
With the death of the Apostles, the keys of the authority of the whole church were taken away. This requires some theological explanation. In the LDS Church, we make a distinction between the priesthood, and the keys of the priesthood. The priesthood itself is something that when it is conferred on someone (assuming it is done by proper authority), it cannot be taken away. He remains a priest forever (unless he commits some very serious transgressions). But the keys of the priesthood is something else that can be taken away. An office in the priesthood is something that confers certain keys on the individual, which he can exercise as long as he holds that office in the Church; and when he is released, those keys are taken away. For example, a bishop has to be a high priest in the Melchizedek priesthood to be ordained a bishop. When he is ordained, he is given the keys to function in that capacity in his own ward (and not in any other). That gives him the right and authority to do certain things pertaining to his calling in his ward. When he is released, those keys are taken away form him; but his priesthood remains. That is not taken away. Those keys always have clearly defined limits and boundaries, and are always delegated and function under the authority of a higher officer. The bishop holds the keys of his office under the authority of the stake president, and he in turn holds the keys of his office under the authority of the President of the Church. The President of the Church is the only one who holds all the keys of all the offices in the Church, and he delegates those keys to other to exercise in their respective callings as he sees fit. He holds those keys in conjunction with his two counsellors who form the First Presidency of the Church. In the absence of the First Presidency, the Quorum of the Twelve Apostles exercise those keys over the Church. Now suppose that through some catastrophic event, all the general leadership of the Church were wiped off the face of the whole earth. What would happen to all the keys of priesthood offices delegated to the rest of the Church? The answer is that they would become dysfunctional. Nobody would hold any keys, until the authority was restored again by divine intervention and angelic ministration to the Church. That is how the priesthood works in the Church. In the early church, with the death of the Twelve Apostles, the keys of authority of the whole church was taken away, and the “laying on of hands” of the ministers of the church no longer conferred any keys, priesthood, or indelible authority to another.
zerinus