Romans 11:16-24
16 For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
17 And if some of the branches be broken off, and thou, being a wild olive tree, wert grafted in among them, and with them partakest of the root and fatness of the olive tree;
18 Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.
19 Thou wilt say then, The branches were broken off, that I might be grafted in.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
22 Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.
23 And they also, if they abide not still in unbelief, shall be grafted in: for God is able to graft them in again.
24 For if thou wert cut out of the olive tree which is wild by nature, and wert grafted contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be grafted into their own olive tree?
This passage from Romans 11 is used as a prooftext for the doctrine that believers can be "broken off" from Christ, and ultimately lose their Salvation, with an emphasis on verses 21 and 22 in particular.
Let's analyze whether that's a valid interpretation.
There are some key passages in the buildup to this point in the book of Romans, which will paint a clearer picture of what the Apostle Paul is saying in the passage in question.
Beginning with the introduction to the book in chapter 1, the Apostle Paul sets the tone for what is a recurring theme in the Epistle - the fact that the Romans are Gentiles, and that he is the Apostle to the Gentiles:
Romans 1:13-16
13 Now I would not have you ignorant, brethren, that oftentimes I purposed to come unto you, (but was let hitherto,) that I might have some fruit among you also, even as among other Gentiles.
14 I am debtor both to the Greeks, and to the Barbarians; both to the wise, and to the unwise.
15 So, as much as in me is, I am ready to preach the gospel to you that are at Rome also.
16 For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek.
This theme is picked up later in the book, when in chapter 9 he begins to lament over the fact that most of his brethren after the flesh, the Jews, do not believe in Jesus:
Romans 9:2-4
2 That I have great heaviness and continual sorrow in my heart.
3 For I could wish that myself were accursed from Christ for my brethren, my kinsmen according to the flesh:
4 Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;
Romans 10:1
1 Brethren, my heart's desire and prayer to God for Israel is, that they might be saved.
Interspersed in this section is the contrasting of the unbelieving Jews with the surprisingly-receptive Gentiles, who have "stepped in the gap", as it were, that was left unfilled by the Jews:
Romans 9:30-32
30 What shall we say then? That the Gentiles, which followed not after righteousness, have attained to righteousness, even the righteousness which is of faith.
31 But Israel, which followed after the law of righteousness, hath not attained to the law of righteousness.
32 Wherefore? Because they sought it not by faith, but as it were by the works of the law. For they stumbled at that stumblingstone;
Romans 10:19-21
19 But I say, Did not Israel know? First Moses saith, I will provoke you to jealousy by them that are no people, and by a foolish nation I will anger you.
20 But Esaias is very bold, and saith, I was found of them that sought me not; I was made manifest unto them that asked not after me.
21 But to Israel he saith, All day long I have stretched forth my hands unto a disobedient and gainsaying people.
However, after discussing this usurpation of the Jews' position by the Gentiles, the Apostle Paul begins chapter 11 with a thought he had started in chapter 10 (Romans 10:12) - that anyone, whether Jew or Gentile, can be saved, and that God has not rejected every Jew just because they are characterized as a people in unbelief:
Romans 11:1-7
1 I say then, Hath God cast away his people? God forbid. For I also am an Israelite, of the seed of Abraham, of the tribe of Benjamin.
2 God hath not cast away his people which he foreknew. Wot ye not what the scripture saith of Elias? how he maketh intercession to God against Israel saying,
3 Lord, they have killed thy prophets, and digged down thine altars; and I am left alone, and they seek my life.
4 But what saith the answer of God unto him? I have reserved to myself seven thousand men, who have not bowed the knee to the image of Baal.
5 Even so then at this present time also there is a remnant according to the election of grace.
6 And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then it is no more grace: otherwise work is no more work.
7 What then? Israel hath not obtained that which he seeketh for; but the election hath obtained it, and the rest were blinded.
Above, we see that there is still hope for the individual Jew, because the issue on the personal level is not really Jew or Gentile, the issue is whether the individual belongs to the "election of grace" (Romans 11:5). Any Jew may go against the grain that characterizes their people by believing in Jesus.
However, the Apostle Paul concludes the thought (Romans 11:7) again discussing "Israel" after the flesh (1 Corinthians 10:18, Romans 9:6), and how though some became a righteous remnant (Romans 10:5), they have been replaced by "the election", which is a cooperate group of Jew and Gentile believers, with a heavy weighting in favor of the Gentiles, to the extent that they now characterize the election, as has been discussed frequently to this point in the book.
He then continues speaking in terms of the Jews and Gentiles as respective groups, again emphasizing that the Gentiles as a people have received the Gospel, along with expressing his desire for, and the potential for, the Jews to do the same:
Romans 11:11-14
11 I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy.
12 Now if the fall of them be the riches of the world, and the diminishing of them the riches of the Gentiles; how much more their fulness?
13 For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office:
14 If by any means I may provoke to emulation them which are my flesh, and might save some of them.
It is only at this point that we arrive at our passage in question.
So, what we have seen in this buildup to our passage in question is the general point taught in the following passage:
1 Peter 2:9-10
9 But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light;
10 Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy.
That point is - the Gentiles, as a group, have accepted the Gospel to the extent that they have now become not only a united "people" under Christ, but now characterize "the people of God" by sheer volume, in distinction from the Jews, to whom that distinction used to belong. They forfeited that distinction by largely rejecting the Messiah which came from them (John 4:22), and was sent to them first (Matthew 10:5-6, 15:24).
Now, another look at the passage in question:
Romans 11:16-24
16 For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches.
17 And if some of the branches be broken off, and thou, being a wild olive tree, wert grafted in among them, and with them partakest of the root and fatness of the olive tree;
18 Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee.
19 Thou wilt say then, The branches were broken off, that I might be grafted in.
20 Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:
21 For if God spared not the natural branches, take heed lest he also spare not thee.
22 Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.
23 And they also, if they abide not still in unbelief, shall be grafted in: for God is able to graft them in again.
24 For if thou wert cut out of the olive tree which is wild by nature, and wert grafted contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be grafted into their own olive tree?
What we see above is not primarily aimed at individuals at all. It's directed towards the Romans only in the sense that they, who were Gentiles, shouldn't see God as having rejected all Jews, as the door is still open to any Jew who wishes to believe in the Messiah.
The passage is a testament to the fact that God's chosen people consists of those who believe in Jesus, whether Jew or Gentile (Galatians 3:28, Colossians 3:11), though the "olive tree", which represents Christ, has now become characterized by these Gentile "grafted-in" branches. This is contrasted with the past, where most of the branches on the "olive tree" were Jewish - and they were "natural branches", because "salvation is of the Jews" (John 4:22) - Jesus was born from them - and is therefore called the "rod out of the stem of Jesse" (Isaiah 11:1, 11:10), and the "root and offspring of David" (Revelation 22:16).
The emphasis is on the fact that although the tables have turned, the new branches should not use this as a means of boasting, because they are only grafted into the "olive tree" by grace (Romans 11:6), because of their faith (Romans 9:30-32), and if in the future their descendants disbelieve, they'll be broken off, just like in the future if the Jews believe, they'll be grafted in again. This looks toward the future generations of both groups.
So, that is the primary application of the passage in question - a recognizing of the fact that the Gentiles are more receptive than the Jews to the extent that they now characterize the body of Christ (the Church - Ephesians 1:22-23, Colossians 1:18, 1:24), but a warning against seeing the Jews as irredeemable, or the Roman Gentiles as seeing themselves as untouchable, in light of that fact. If their descendants, along with the descendants of other receptive Gentiles, cease believing in Jesus, then the group that characterizes the "olive tree" may well shift back in favor of the Jews, as it had once been, when they believed.
A secondary application that this passage can be used to teach on relates to something Jesus said in John chapter 15:
John 15:1-8
1 I am the true vine, and my Father is the husbandman.
2 Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit.
3 Now ye are clean through the word which I have spoken unto you.
4 Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
5 I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
6 If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned.
7 If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you.
8 Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples.
I cover this passage in its own article as well, but the gist of what Christ is saying here is in reference to the fact that if an individual fails to abide in Christ, they will spiritually "wither", fail to "bear fruit", and ultimately, turned over for the "destruction of the flesh" (1 Corinthians 5:5), as God will not tolerate dead branches on the vine (James 2:17).
In this application, we can view the verses mentioning being "cut off" from our passage in question (Romans 11:20-22) as paralleling this chastening of a wayward believer, who is not abiding, which may ultimately result in physical death (1 Corinthians 11:30-32).
In no way can either passage refer to a believer going to Hell when they die, as evidenced by the fact that we already have clear promises that a believer "shall never die" (John 11:26, 6:50), "shall never perish" (John 10:28), "has Everlasting Life" (John 3:15-16, 3:36, 5:24, 6:40, 6:47, 6:54), "shall live forever" (John 6:51, 6:58), and so on - all promises which God will faithfully uphold even if a believer stops believing (2 Timothy 2:13) - as discussed in many other places on this site.
Though primarily discussing two groups of people - Jews and Gentiles - and their representation in the body of Christ, this passage may also be used to teach on an individual believer's need to abide in Christ after Salvation.
In neither circumstance does it teach a loss of Salvation, but rather serves as a warning to continue to abide in Christ, lest a group lose their exalted position in Christ through unbelief, or an individual loses their chance to serve God through failing to abide.