*Verse 39 - But we are not of those who draw back to perdition, but of those who believe to the saving of the soul. Those who draw back to perdition do not believe to the saving of the soul and those who believe to the saving of the soul do not draw back to perdition.
From beginning "have been saved through faith" (Ephesians 2:8) to end "receiving the end of your faith--the salvation of your souls" (1 Peter 1:9) salvation is through faith and is not by works. Now once again, James is not using the word "justified" to mean "accounted as righteous" but is "shown to be righteous." James is discussing the proof of faith (says-claims to have faith but has no works/I will show you my faith by my works - James 2:14-18), not the initial act of being accounted as righteous with God (Romans 4:2-3). Works bear out the justification that already came by faith.
People who draw back to perdition do not believe to the saving of the soul, which is not proper faith. Shallow, temporary belief that has no root and draws back to perdition was never saving faith in Christ to begin with. Either we are in the flesh and cannot please God or else we are in the Spirit and belong to Christ (Romans 8:6-10).
The Jews were in the olive tree to begin with because they were the "natural branches" and not because they were all saved. Because of their unbelief and hard hearts God removed His gracious hand from them as a people overall and broke them off from His goodness (but only for a time after which they will be restored). We Gentiles have now been grafted into God's goodness and are the recipients of His blessings. Paul's warning is that we should not get arrogant because we might lose the goodness and blessings of God just like the Jews lost the goodness and blessings of God -- but this doesn't speak of losing salvation.
*Notice - Brethren, if anyone "among" you wanders from the truth..turns a "sinner" from the error of his way.. Some would argue that James says this one who turned from the truth was a "sinner," and was "among" but "not of" the Brethren, then he wasn’t previously saved. That fits 1 John 2:19 - They went out "from" us, but they were "not of" us..
IF this person was a genuine believer, yet how do we know for sure this is the second death in the lake of fire? In Matthew 26:38, Jesus said: "My soul [psuche] is deeply grieved, to the point of death." Jesus was not saying that His soul was deeply grieved to the point of spiritual death, Rather, Jesus was talking about physical death, his human life. In Revelation 16:3, "The second angel poured out his bowl into the sea, and it became blood like that of a dead man; and every living soul [psuche] in the sea died". In 1 Peter 3:20 "... God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, [psuche-souls] were brought safely (saved from drowning, physical death) through the water" by the ark (Hebrews 11:7).
"Soul" is rendered from the Greek word "psuche" and is also translated as "life". The word "psuche" is never translated as "spirit." In 1 Corinthians 5:5, we read - I have decided to deliver such a one to Satan for the destruction of his flesh, (physical death) so that his spirit may be saved in the day of the Lord Jesus (no second death).
Jesus covered our sins in one way (Romans 4:7) by bringing forgiveness for all believers, yet sins can also be covered in a different way. In Proverbs 10:12, we read: Hatred stirs up strife, But love covers all sins. In 1 Peter 4:8, we read: And above all things have fervent love for one another, for "love will cover a multitude of sins." Where there is strife, there is hatred and unless love prevails, the strife will get worse. Love covers offenses and sins when a believer turns back from error.
So is this wanderer a professing Christian, whose faith is not genuine, or a sinning Christian, who needs to be restored? For the former, the death spoken of in vs. 20 is the "second death" (Revelation 21:8); for the latter, it is physical death (1 Corinthians 11:29-32; 1 John 5:16).