We know that the three Nephites will minister both among the Gentiles and to the House of Israel. That they are alive today—working miracles on behalf of the Lord and performing great and marvelous works (v. 31)—is a sobering thought. Indeed, this is the stuff that legends are made of. It is also the stuff that rumors and Mormon “urban legends” are made of. Who hasn’t heard a story about how one of the three Nephites appeared to someone in our day? Unfortunately, most of these stories are highly suspect. One example is given:
“The ‘Nephites on the Mesa’ [story] has also been around for at least thirty years. Supposedly some good members driving to conference are stopped in the desert between Las Vegas and St. George by a man dressed in black. The stranger warns the members to accomplish some spiritual goal (food storage, genealogy, and so on) by a certain date because something apocalyptic is about to happen. The man in black then asks to be let out, and as the car drives away, he vanishes from sight. Obviously, he was one of the Three Nephites. Less obvious is why these instructions for the Church didn’t come through the proper channels…Once again—the Lord does not govern his people by rumor.” (Stephen R. Robinson, Following Christ, p. 107-8)
So we should not expect the three Nephites to appear to us and tell us to move to Missouri. That is not their calling and ministry. They have been doing greater and more magnificent things for the Lord even throughout the Great Apostasy.
Joseph Fielding Smith
"It is reasonable to believe that they were engaged in this work as far as the Lord permitted them to go during these years of spiritual darkness (the Great Apostasy). There are legends and stories which seem to be authentic, showing that these holy messengers were busy among the nations of the earth, and men have been entertained by them unawares. We may also well believe that these translated prophets have always been busy keeping constraint upon the acts of men and nations unbeknown to mortal man.
“Translated beings have not passed through death; that is, they have not had the separation of the spirit and the body. This must wait until the coming of the Savior. In the meantime they are busy fulfilling their glorious mission in preparing the way for the elders of Israel to go forth with the message of salvation in all parts of the world.” (Answers to Gospel Questions, vol. 2, p. 46)
Elder John W. Taylor
“…in a little while you will find another prophecy will be fulfilled, and that is the prophecy that Jesus made to the three Nephites who, having power over death, are still living upon this continent. He spoke to them of a time when they would perform a great and mighty work among the Gentiles; and that has not yet been fulfilled, but it will be. You will find that many districts where the Elders of Israel cannot reach will be penetrated by these men who have power over death…My testimony is that these men are going abroad in the nations of the earth before the face of your sons, and they are preparing the hearts of the children of men to receive the Gospel. They are administering to those who are heirs of salvation, and preparing their hearts to receive the truth, just as the farmer prepares the soil to receive the seed. The Lord has promised that He would send his angels before the face of His servants, and His does so.” (Conference Report, Oct. 1902, p. 75 as taken from Latter-day Commentary on the Book of Mormon compiled by K. Douglas Bassett, p. 463)