In the Book of Mormon, there was a small group of people whose ethnic/religious lineage was preserved throughout the span of the history of the account.

3 Nephi 5:20 I am Mormon, and a pure descendant of Lehi.

This means, that like his Jewish predecessors who were obedient to God’s law back in Jerusalem, his fathers going all the way back to Lehi, did not mix with lineages outside their own. Lehi was a descendant of Manasseh, who was the son of Joseph who was the son of Jacob whose name was changed to Israel. In the title page, being on the last leaf of the gold plates upon which is an account written “by the hands of Mormon taken from the plates of Nephi,” we read that the record is an account of the people of Nephi (who was Lehi’s son), the covenant people of God, being blessed according to their obedience to God’s laws and also a record of the Lamanites, who were not obedient covenant people. The Lamanites consisted of all who were dissented from the people of Nephi. Or as Jacob described:

Jacob 1:13 Now the people which were not Lamanites were Nephites; nevertheless, they were called Nephites, Jacobites, Josephites, Zoramites, Lamanites, Lemuelites, and Ishmaelites.
14 But I, Jacob, shall not hereafter distinguish them by these names, but I shall call them Lamanites that seek to destroy the people of Nephi, and those who are friendly to Nephi I shall call Nephites, or the people of Nephi, according to the reigns of the kings.   

With the exception of Zoram who was not a son of Lehi, and the children of Ishmael, all others were Lehi’s children. And all who dissented and sought to destroy Nephi and his covenant keeping posterity were called Lamanites by the Nephites. Continuing with the title page of the Book of Mormon, we read that it was primarily–or at least written first and foremost–for the Lamanites or as we read:

“Written to the Lamanites, who are a remnant of the house of Israel; and also to Jew and Gentile.”

Nephi and all his posterity considered themselves Jews:

2 Nephi 33:8 I have charity for the Jew—I say Jew, because I mean them from whence I came…

We are reading their record from their own perspective. The final record keeper, Moroni, who was Mormon’s son, considered himself a Nephite, a pure descendant of Lehi who was Jewish. Therefore he distinguishes the Lamanites from the Jews who in his own time had dwindled in unbelief, or in other words, became extinct. Moroni also includes the Gentile, those outside the covenant made to his fathers. It is through the Gentiles that the record would come forth and so it did.

While there are undoubtedly a number of remnants of Israel scattered throughout the world, the Nephite prophets and record keepers knew that their words were intended for their brethren the Lamanites who would be preserved. Nephi indicates as much quoting his father Lehi:

2 Nephi 1:5 But, said he, notwithstanding our afflictions, we have obtained a land of promise, a land which is choice above all other lands; a land which the Lord God hath covenanted with me should be a land for the inheritance of my seed. Yea, the Lord hath covenanted this land unto me, and to my children forever, and also all those who should be led out of other countries by the hand of the Lord.

The same promise was made to Lehi’s grandson, Enos:

Enos 1:16 And I had faith, and I did cry unto God that he would preserve the records; and he covenanted with me that he would bring them forth unto the Lamanites in his own due time.
17 And I, Enos, knew it would be according to the covenant which he had made; wherefore my soul did rest.
18 And the Lord said unto me: Thy fathers have also required of me this thing; and it shall be done unto them according to their faith; for their faith was like unto thine.

And so Lehi blessed his posterity who would dissent from the covenant because of the wickedness of their parents:

2 Nephi 4:3 Wherefore, after my father had made an end of speaking concerning the prophecies of Joseph, he called the children of Laman, his sons, and his daughters, and said unto them: Behold, my sons, and my daughters, who are the sons and the daughters of my firstborn, I would that ye should give ear unto my words.
4 For the Lord God hath said that: Inasmuch as ye shall keep my commandments ye shall prosper in the land; and inasmuch as ye will not keep my commandments ye shall be cut off from my presence.
5 But behold, my sons and my daughters, I cannot go down to my grave save I should leave a blessing upon you; for behold, I know that if ye are brought up in the way ye should go ye will not depart from it.
6 Wherefore, if ye are cursed, behold, I leave my blessing upon you, that the cursing may be taken from you and be answered upon the heads of your parents.
7 Wherefore, because of my blessing the Lord God will not suffer that ye shall perish; wherefore, he will be merciful unto you and unto your seed forever.
8 And it came to pass that after my father had made an end of speaking to the sons and daughters of Laman, he caused the sons and daughters of Lemuel to be brought before him.
9 And he spake unto them, saying: Behold, my sons and my daughters, who are the sons and the daughters of my second son; behold I leave unto you the same blessing which I left unto the sons and daughters of Laman; wherefore, thou shalt not utterly be destroyed; but in the end thy seed shall be blessed.

Lehi’s patriarchal blessing ensured that his posterity would not perish, but rather they would be preserved “forever.” And it is this posterity–the Lamanites–which is spoken about and it is they who are referred to throughout the record as the “remnant” or the “remnant of Joseph.” Jesus Christ addresses this remnant when He teaches the people at Bountiful in the flesh. And it is this remnant whom Moroni personally addresses in his final pages:

Moroni 10:1 Now I, Moroni, write somewhat as seemeth me good; and I write unto my brethren, the Lamanites; and I would that they should know that more than four hundred and twenty years have passed away since the sign was given of the coming of Christ.
2 And I seal up these records, after I have spoken a few words by way of exhortation unto you.
3 Behold, I would exhort you that when ye shall read these things, if it be wisdom in God that ye should read them, that ye would remember how merciful the Lord hath been unto the children of men, from the creation of Adam even down until the time that ye shall receive these things, and ponder it in your hearts.
4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.
5 And by the power of the Holy Ghost ye may knowthe truth of all things.
6 And whatsoever thing is good is just and true; wherefore, nothing that is good denieth the Christ, but acknowledgeth that he is.
7 And ye may know that he is, by the power of the Holy Ghost; wherefore I would exhort you that ye deny not the power of God; for he worketh by power, according to the faith of the children of men, the same today and tomorrow, and forever.
8 And again, I exhort you, my brethren, that ye deny not the gifts of God, for they are many; and they come from the same God. And there are different ways that these gifts are administered; but it is the same God who worketh all in all; and they are given by the manifestations of the Spirit of God unto men, to profit them.
9 For behold, to one is given by the Spirit of God, that he may teach the word of wisdom;
10 And to another, that he may teach the word of knowledge by the same Spirit;
11 And to another, exceedingly great faith; and to another, the gifts of healing by the same Spirit;
12 And again, to another, that he may work mighty miracles;
13 And again, to another, that he may prophesy concerning all things;
14 And again, to another, the beholding of angels and ministering spirits;
15 And again, to another, all kinds of tongues;
16 And again, to another, the interpretation of languages and of divers kinds of tongues.
17 And all these gifts come by the Spirit of Christ; and they come unto every man severally, according as he will.
18 And I would exhort you, my beloved brethren, that ye remember that every good gift cometh of Christ.
19 And I would exhort you, my beloved brethren, that ye remember that he is the same yesterday, today, and forever, and that all these gifts of which I have spoken, which are spiritual, never will be done away, even as long as the world shall stand, only according to the unbelief of the children of men.
20 Wherefore, there must be faith; and if there must be faith there must also be hope; and if there must be hope there must also be charity.
21 And except ye have charity ye can in nowise be saved in the kingdom of God; neither can ye be saved in the kingdom of God if ye have not faith; neither can ye if ye have no hope.
22 And if ye have no hope ye must needs be in despair; and despair cometh because of iniquity.
23 And Christ truly said unto our fathers: If ye have faith ye can do all things which are expedient unto me.

After this, Moroni addresses everyone else:

24 And now I speak unto all the ends of the earth—that if the day cometh that the power and gifts of God shall be done away among you, it shall be because of unbelief…

Of this remnant of Joseph, Orson Pratt had the following to say:

“We can pray to the Father, in the name of Jesus, to convert these Indian tribes around us, and bring them to a knowledge of the truth, that they may fulfill the things contained in the Book of Mormon. And then when we do return, taking them with us, that they shall be instructed not only in relation to their fathers and the Gospel contained in the record of their fathers, but also in the arts and sciences. They will also be instructed to cultivate the earth, to build buildings as we do, instructed how to build Temples and in the various branches of industry practiced by us; and then, after having received this information and instruction, we shall have the privilege of helping them to build the New Jerusalem. The Lord says—“They,” the Gentiles, who believe in the Book of Mormon, “shall assist my people, the remnant of Jacob, that they may build a city, which shall be called the New Jerusalem.”

Now, a great many, without reading these things, have flattered themselves that we are the ones who are going to do all this work. It is not so; we have got to be helpers, we have got to be those who cooperate with the remnants of Joseph in accomplishing this great work; for the Lord will have respect unto them, because they are of the blood of Israel, and the promises of their fathers extend to them, and they will have the privilege of building that city, according to the pattern that the Lord shall give…We have got to be sent forth as missionaries to all parts of this American continent. Not to the Gentiles, for their times will be fulfilled; but we must go to all those tribes that roam through the cold regions of the north—British America, to all the tribes that dwell in the Territories of the United States, also to all those who are scattered through Mexico, and Central and South America, and the object of our going will be to declare the principles of the Gospel unto them, and bring them to a knowledge of the truth…

These are some few things pertaining to the redemption of Zion. I would to the Lord that we were righteous enough to know a few more! There are a great many things that I would like to know about the redemption of Zion that I do not know, and I presume that you also would like to know them. But what the Lord has revealed is very plain when connected together; and when we reflect upon it, it is astonishing to us to think that in our day the Lord has decreed to perform such a great work in the midst of the earth. It will be astonishing to us when the time comes for the Lord to gather in, from every part of this great continent, these poor, miserable, degraded Lamanites, that his servants may have power over them in order to bring them to civilization. It looks impossible to us, but remember that that is the day of the Lord’s power, and that then will be fulfilled the saying in the Book of Doctrine and Covenants, that the Spirit of the Lord shall be shed forth upon the hearts of those who are ordained to that power; that every man among these remnants of Joseph will hear the Gospel in his own tongue, by the power of the Holy Ghost shed forth upon those who are ordained unto this power. There is such a saying as that in the Book of Covenants, and when that day comes the Lord God will work mightily by signs, wonders and miracles in various ways that will have an influence over these remnants of Joseph to convert them and bring them to a knowledge of the truth, that the prayers of their ancient fathers, and of the Prophets and Elders who once dwelt on this American continent, may be fulfilled upon their heads.”  (source: http://jod.mrm.org/17/289)

In 3 Nephi 21, Jesus Christ declared as much during His visit to Bountiful. Finally, I wish to add:

D&C 49:24 But before the great day of the Lord shall come, Jacob shall flourish in the wilderness, and the Lamanites shall blossom as the rose.