Philippians 1:3-6
3 I thank my God upon every remembrance of you,
4 Always in every prayer of mine for you all making request with joy,
5 For your fellowship in the gospel from the first day until now;
6 Being confident of this very thing, that he which hath begun a good work in you will perform it until the day of Jesus Christ:
The Grace New Testament Commentary - Philippians 1:6
1:6 Paul's settled conviction is that this good work of the Philippians will be carried on until the day of Jesus Christ. Christ Himself is the agent of this good work. He began the good work by placing within the church ("you" is plural) the desire to help the one (Paul) who had led them to Christ. Then Christ continues this work through Paul so that the ongoing effects of their good work will end only at the day of Jesus Christ, that is, at the Judgment Seat of Christ. Their partnership with Paul will continue long after they (and Paul) have died and gone to heaven. The ultimate effects will only be seen at the Judgment Seat of Christ.
A common view of this verse is that sanctification of believers is a guaranteed work of God. However, a preferable view is that this is a promise that the Lord will honor and bless the missionary efforts of the Church in ways far beyond what it can see or understand.
Thomas Constable's Expository Notes on the Bible - Philippians 1:6
What was the good work to which Paul referred in this verse? If he had in mind only the generosity of his original readers he may have meant that good work. However, as I have suggested, he seems to have had a much broader concept in mind: what the work of the gospel produces, namely, salvation. Who was the He who had begun this good work of salvation? It could only be God. Paul was confident that God would complete what He had begun in his beloved Philippians.
In the New Testament God has revealed that salvation is a process. It involves justification, which takes place when a sinner trusts Jesus Christ as his or her Savior. It also includes progressive sanctification, which occurs continuously from the time of justification until the Christian's death or the Rapture. And it culminates in glorification, when the redeemed sinner finally sees Jesus Christ and experiences transformation into His image. Paul was confident that just as surely as God had justified the Philippians He would also continue to sanctify and eventually glorify them. Whereas we have a hand in the process of sanctification, and can affect it by our obedience or disobedience, God alone justifies us. Regardless of our carnality or spirituality He will also glorify us (1 Cor. 15:50-57).
The aspect of sanctification that Paul had in view, in view of verse 5, was the Philippians' partnership with him in the work of propagating the gospel. He was confident that God would continue His sanctifying work in them so that they might become even more effective partners with him in this great task.
This verse does not teach that God will keep all Christians faithfully persevering in the faith and in good works until they die. Believers can and do resist, oppose, and limit God's sanctifying work in them (Eph. 4:30: 1 Thess. 5:19). Perseverance in faith and good works is not automatic for the Christian. The New Testament writers consistently urged us to persevere recognizing that some Christians will not do so (Titus 2:11-13; Heb. 2:1; 4:1; 6:1-8; et al.). Even some of Paul's fellow workers did not persevere faithfully (1 Tim. 1:18-20: 2 Tim. 2:17-18; 4:10). Even though some Christians do not persevere in faith and good works, God will persevere in bringing them to glory: He will glorify them. Thus it is God who perseveres in the work of salvation, not necessarily people.