Good works are not part of the Gospel (Ephesians 2:8-9), they're not requirements for salvation, rather they're the fruits of salvation. Paul calls the Philippians to work out their salvation in Philippians 2:12. However, this is not a call to do works in order to be saved, rather it is a call for them to evaluate their lifestyle and see whether it is in accordance with their salvation. In other words, if good works are non-existent, then there is good reason for one to call into question whether or not he/she was ever saved in the first place. The gospel brings transformation, as Paul tells us in Ephesians 4:17-32; therefore, if someone claims to be a Christian, but does not live like one, then there is serious reason to believe he is not one (especially if he will not listen to correction). Once a person is saved, however, and God writes his name in the book of life and gives him the Spirit, he won't erase their name from the book of life.
One interesting way to think of this is the pictures of the Old Testament. In the animal sacrifices, which God commands of Israel, the man was to place his hand on the lamb's head, signifying that his sin was being passed to the lamb, then the lamb would be killed in place of the man. If one can lose their salvation, the image might be reversed to be a man kneeling with his head bowed and a lamb with his paw on the man's head passing the sin back to the man. John the Baptist makes the connection of Christ with this image when he says, "Behold the Lamb of God, which taketh away the sin of the world" (John 1:29). Notice that John says nothing about him giving the sin back to the world, once he takes it away, he does not return it.That's how I see this. Feel free to comment on this.
You seem to see sin as a physical object -- either you have it or you don't -- and that it can be passed from one person to another. Yet, notice what is actually stated:
"Speak to the sons of Israel and say to them, 'When any man of you brings an offering to the LORD, you shall bring your offering of animals from the herd or the flock. If his offering is a burnt offering from the herd, he shall offer it, a male without defect; he shall offer it at the doorway of the tent of meeting, that he may be accepted before the LORD. He shall lay his hand on the head of the burnt offering, that it may be accepted for him to make atonement on his behalf'" (Leviticus 1:2-4).
There is no mention of his sins being passed to the animal. The animal does stand in for the man to make atonement on his behalf, but it doesn't say the animal carries the man's sins away. Instead, we know that animal sacrifices did not remove sins. "For it is impossible for the blood of bulls and goats to take away sins" (Hebrews 10:4).
To be in sin is a state of being, not an object. Sin is the breaking of God's law. "Everyone who practices sin also practices lawlessness; and sin is lawlessness" (I John 3:4). You cannot give sin back, but a forgiven person may break the law again and once again be in sin.
A person can be restored to a right relationship with God by the forgiveness of his sins through the blood of Jesus. "If we say that we have fellowship with Him and yet walk in the darkness, we lie and do not practice the truth; but if we walk in the Light as He Himself is in the Light, we have fellowship with one another, and the blood of Jesus His Son cleanses us from all sin" (I John 1:6-7).
While John said "Behold, the Lamb of God who takes away the sin of the world!" (John 1:29), there is more here that you might first realize. Notice that John is not talking about an individual but the whole world. Also notice that he says "sin" and not "sins". In the Old Testament, there was a yearly sacrifice of a goat. "Then he shall slaughter the goat of the sin offering which is for the people, and bring its blood inside the veil and do with its blood as he did with the blood of the bull, and sprinkle it on the mercy seat and in front of the mercy seat. He shall make atonement for the holy place, because of the impurities of the sons of Israel and because of their transgressions in regard to all their sins; and thus he shall do for the tent of meeting which abides with them in the midst of their impurities" (Leviticus 16:15-16). Where the Old Testament atonement was for Israel's sins, Jesus came for the sins of the whole world. John was saying that Jesus would be the atonement sacrifice of the entire world. By using the singular, John is emphasizing that it is a single sacrifice to deal with the complete problem of sin.
Sin is something done, it is something practiced. But righteousness is also something done. Notice the condition is I John 1:7, "if we walk in the Light." The result is that we have fellowship with fellow Christians and cleansing from sin. "So then, my beloved, just as you have always obeyed, not as in my presence only, but now much more in my absence, work out your salvation with fear and trembling; for it is God who is at work in you, both to will and to work for His good pleasure" (Philippians 2:12-13). I'm amazed at the lengths you went to avoid what Paul said. There is nothing here about questioning whether one is saved or not. Paul states that God is at work in the Christian and He commands that Christians both desire to do God's commands and to work on them.
I agree that these works do not earn a person's salvation. "He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit, whom He poured out upon us richly through Jesus Christ our Savior, so that being justified by His grace we would be made heirs according to the hope of eternal life" (Titus 3:5-7). At the best we can only claim that we are doing what God commanded us to do. "So you too, when you do all the things which are commanded you, say, 'We are unworthy slaves; we have done only that which we ought to have done'" (Luke 17:10). Notice that not working isn't an option; that is what the lazy servant learned. "But his master answered and said to him, 'You wicked, lazy slave, you knew that I reap where I did not sow and gather where I scattered no seed. Then you ought to have put my money in the bank, and on my arrival I would have received my money back with interest. Therefore take away the talent from him, and give it to the one who has the ten talents.' For to everyone who has, more shall be given, and he will have an abundance; but from the one who does not have, even what he does have shall be taken away. Throw out the worthless slave into the outer darkness; in that place there will be weeping and gnashing of teeth" (Matthew 25:26-30). It was a lack of work that caused this servant to lose his salvation.
When Israel sinned while Moses was on Mount Sinai, Moses was so upset that he broke that tablets containing the Ten Commandments. However, he approached God to ask Him to forgive Israel, and if God would not, Moses asked that he not be saved either. "Then Moses returned to the LORD, and said, "Alas, this people has committed a great sin, and they have made a god of gold for themselves. But now, if You will, forgive their sin -- and if not, please blot me out from Your book which You have written!"" (Exodus 32:31-32). God refused Moses' request. No one is removed because he asks to be removed. "The LORD said to Moses, "Whoever has sinned against Me, I will blot him out of My book"" (Exodus 32:33). Notice that there is a reason that someone's name is removed from the book. Sin can cause a person's name to be removed. This flatly contradicts what you had claimed.
Consider the warning that Jesus gave the Christians in Sardis: "To the angel of the church in Sardis write: He who has the seven Spirits of God and the seven stars, says this: 'I know your deeds, that you have a name that you are alive, but you are dead. Wake up, and strengthen the things that remain, which were about to die; for I have not found your deeds completed in the sight of My God. So remember what you have received and heard; and keep it, and repent. Therefore if you do not wake up, I will come like a thief, and you will not know at what hour I will come to you. But you have a few people in Sardis who have not soiled their garments; and they will walk with Me in white, for they are worthy. He who overcomes will thus be clothed in white garments; and I will not erase his name from the book of life, and I will confess his name before My Father and before His angels'" (Revelation 3:1-5). Jesus told them that their deeds were not complete. They needed to change. If they overcome this problem then Jesus would not erase their names from the book of Life. But that also means those who did not change by doing the work completely that they were required to do would be removed. This is clearly not a statement that these people were never Christians in the first place.