The atonement has power to save those in a state of innocence. In particular, this applies to two main groups, little children (v. 16) and those who have not the law given to them (2 Nephi 9:26). This principle is taught in the law of sacrifice as found in the law of Moses, If a soul shall sin through ignorance against any of the commandments of the Lord….[the priest] shall do with the bullock as he did with the bullock for a sin offering…the priest shall make an atonement for them, and it shall be forgiven them (Lev 4:2,20).
The Book of Mormon teaches this principle in several different locations. King Benjamin's sermon includes the following, his blood atoneth for the sins of those who have fallen by the transgression of Adam, who have died not knowing the will of God concerning them, or who have ignorantly sinned. Mormon teaches that both children and those without the law will be saved, For behold that all little children are alive in Christ, and also all they that are without the law, for the power of redemption cometh on all them that have no law (Moroni 8:22).
The scriptures go so far as to say that those without the law will come forth in the first resurrection, And then shall the heathen nations be redeemed, and they that knew no law shall have part in the first resurrection; and it shall be tolerable for them (DC 45:54). They will come forth in the first resurrection after those who are "the first fruits" (or those who come forth in the morning of the first resurrection). For the most part, they will inherit the terrestial kingdom and will be resurrected as "those who are Christ's at his coming' (DC 88:98-9) (or those who come forth in the afternoon of the first resurrection). This conclusion can be made by studying the following scriptures, DC 88:98-9, DC 76:71-73, Mosiah 15:24-25, Heb 5:2, DC 137:7, and Mormon Doctrine, p. 640.