Here the editors for the 1920 LDS edition emended people’s to peoples’. The change is marked in the 1920 committee copy, so it was intentional. This change was perhaps made under the influence of the subsequent plurals (the edited plural verb form are and two instances of the plural possessive pronoun their). But nowhere else in the text are there any instances of the plural peoples (nor the possessive plural peoples’ ). We get only the singular form people, even though it occurs with both singular and plural demonstrative adjectives (as “this people” and “these people”) and singular and plural verbs (“people is” and “people are”). There are no other examples in the text of “the people’s sake”, but there is one of “for the sake of our people” (in Jacob 1:4). The singular possessive people’s is undoubtedly the correct form here in Helaman 13:17. Don Brugger points out (personal communication) that here in Helaman 13 (see verses 5–16) Samuel the Lamanite is speaking to only one people, namely, the Nephites, as is specifically noted in the immediately preceding verse: “yea and woe be unto all the cities which are in the land round about which is possessed by the Nephites because of the wickedness and the abominations which is in them” (Helaman 13:16).
We should also note here the use of the relative pronoun which (later edited to who) to refer to people rather than to the nearest noun (sake). Another example where the relative pronoun does not refer to sake but to the preceding noun (in this case Christ ) is found in Alma 4:13: “and suffering all manner of afflictions for Christ’s sake which should come according to the spirit of prophecy”.
Summary: Restore in Helaman 13:17 the 1830 spelling people’s; the Book of Mormon never uses the plural peoples, much less the possessive plural peoples’.