There is every reason to think that those who have believed in Jesus Christ as Savior and are consequently born into God's family will experience a changed life to some degree. Some would say that this changed life is evidenced by good works which proves they are saved. If that is true, then the converse is true: if there are no good works, then there is no salvation. In this view, good works (sometimes called "fruit" or evidence of a changed life) prove or disprove one's eternal salvation.
Some passages are used to contend that works can prove or disprove one's eternal salvation. Probably the most common are James 2:14-26, John 15:6, and Matthew 7:15-20. But James is writing to Christians about the usefulness of their faith, not its genuineness. Likewise, in John 15:6 Jesus is talking about fruitless believers and compares them to branches that are burned, in other words, not of much use. Matthew 7:15-20 warns against false prophets (not believers in general) who can be evaluated on the basis of their evil deeds or heretical teaching (not an absence of works in general).
There is no passage of Scripture that claims works can prove salvation. In fact, there are many problems with trying to use works to prove salvation, or the lack of works to disprove salvation.
Good works can characterize non-Christians. Works in and of themselves can not prove that anyone is eternally saved because those who have not believed in Christ will often do good things. In fact, good deeds are essential to many non-Christian religions. Sometimes the outward morality of non-Christians exceeds that of established Christians. In Matthew 7:21-23 we see the possibility of those who do not know Christ doing great works, but their works are useless in demonstrating their salvation; they are not saved.
Good works can be hard to define. Though we might define a good work as something done by a Christian through the Spirit for the Lord, how can we always know when that is true? It is hard to imagine even a single day when a Christian (or non-Christian, for that matter) would not do something good like go to work to provide for a family, hold a door for someone, or brake for a squirrel. How can we know when these things are done through the Spirit and for the Lord, especially if they can be done by non-Christians?
Good works are relative. While a person's behavior may seem excessive, it may actually demonstrate great progress in that person's Christian growth. A man slips with a curse word that startles other believers, but those believers do not know that before his conversion, curse words flowed freely. The amount of fruit must be considered in the context of one's total past life, a difficult thing to do. It may also be relative to the amount of sin in one's present life. For example, if a Christian were to commit adultery, we might focus our thinking on that sin so that we ignore the other good things he is doing.
Good works can be passive in nature. The fruit of salvation is not always what we do, but often what we do not do. As a Christian, one may no longer get drunk or may refrain from yelling at an inconsiderate motorist. This fruit of the Spirit, self-control, may not be detected by others because of its passive nature.
Good works can be unseen. In Matthew 6:1-6 Jesus told his followers to give and pray in secret rather than publicly. A person who never prays in a group may breathe a prayer while driving and no one will ever know. Another may not attend church, but give regularly to a Christian charity. These are works that go unobserved by others.
Good works can be deceptive. Since we can not know one's motives, a seeming good work could be done for the wrong reason. A person might give money to a church to impress others. Another might volunteer to work with church children only to wait for an opportunity to sexually abuse them. These are not actually good works at all! Motives are difficult to discern, even for the doer, but God knows each person's heart (1 Cor. 4:3-5)
Good works can be inconsistent. The Bible allows the possibility of believers who begin well, but fall away from their walk with the Lord or fall into sin (1 Cor. 11:30; 2 Tim. 4:10; James 5:19-20). If a Christian shows the evidence of a changed life, but later falls away, at what point in their life do we examine them to prove or disprove their salvation? If there can be lapses in good works, how long does the lapse continue before one is judged as never saved?
Nowhere does the Bible teach that fruit or good works can prove one's eternal salvation. Since the fruit of good works is not easily discerned or quantified, it can not be reliable proof of salvation. The subjective nature of measuring one's fruit creates the impossibility of knowing objectively whether someone is saved. The amount of fruit necessary to please one Christian "fruit inspector" may not please the next "fruit inspector." As Christians, we are created in Jesus Christ to do good works (Eph. 2:10) and expected to do good works (1 Tim. 6:18; Titus 2:7, 14; Heb. 10:24), but good works are never attached to the condition for salvation, which is faith alone in Christ alone (Rom. 4:4-5). While good works can be corroborating evidence for one's faith in Christ, they are not sufficient to prove or disprove it. Only faith in God's promise of eternal life through Jesus Christ guarantees and proves our salvation.