It is the broken and contrite spirit that Jesus will in no wise cast out. Your phrasing initially was tricky and I missed the trick. You place 'has faith' alongside unrepentant, where it does not belong. But I see it now. You wrote/questioned:
If someone has faith yet is still attached to sin, is he saved? Is the unrepentant adulterer who has faith saved? Is the unrepentant murderer who has faith saved?
To come to faith in the Lord Jesus Christ you must recognize you are a hopeless sinner and that your only hope is in Jesus Christ. Without getting bogged down in picking at nits, the broken and contrite spirit is a work of The Lord. No man comes to the Father but by Jesus. God draws to Jesus those whom God chooses. God breaks the sinner making them broken and contrite.
Contrition of the sinner is the 'thing' God produces so that the soul of the sinner turns to Jesus for Salvation. The work that God does to bring one to the contrition state will harden the soul that rejects their need for Jesus Christ, and too many believe they can be good enough for God's measure without allowing God to bring them to the point of contrition. That is the picture of the unrepentant soul, the one who will not let God bring them tot he point of contrition.
The unrepentant soul is displayed clearly in one Simon Magus. The Bible says that magician believed and was also baptized. But he was unrepentant, he was tasting of the new way but not allowing God's Spirit to bring him to the state of contrition. You can do a Bible search on Simon and see how God dealt with his belief but unrepentant heart. However, even Simon was brought to repentence, showing how Merciful God is. So, to answer the question I misread to start with, my answer is/God's answer is, the unrepentant soul is not yet ready to be delivered from their sin, their sin nature.
This is a very crucial issue you've raised and I'm glad/I thank you that you continued on in this issue since it really is vital to understand The Gospel of God's Grace in Christ. No lifetime of works is going to change an unrepentant heart, because ONLY God brings the sinner to the point of repenting and believing in Jesus as The Christ, The Son of the Living God. It is God's Holy Spirit Who brings the heart to the state of contrition that meets repentence. Now, what is the result of the broken and contrite spirit when it comes to Christ? Let's see what else you wanted to focus upon:
The one lacks the love to forgive others is also save.
I will presume you meant 'also saved'. When a broken and contrite spirit is born from above, they are not yet in a state of perfection, able to love the way God loves. They are to be raised up in the Way that they should go by the present in them Holy Spirit. Try not to conflate the unrepentant with the born from above one not yet able to love with agape. It leads to false conclusions ...
How do you reconcile this with what Jesus said: "If you forgive others their transgressions, your heavenly Father will forgive you. But if you do not forgive others, neither will your Father forgive your transgressions." [The Bema Seat of Christ IN HEAVEN will feature some very interesting effects of the Shekinah Glory of God shined upon the life of the Saved, Raptured, family members.] Or with his declaration that if we are to enter into eternal life we must keep the commandments.
Now let's look at a false conclusion you reached by my clumsy misreading of your initial questions and the application of the false trail you want me to follow:
You need to stop trying to force that round peg of sola fide into the square whole of Scripture. Sola fide is a manmade tradition that is contrary to Scripture."
Pegs and 'whole' aside, the Bible very clearly and repeatedly tells you that it is by God's Grace that your are Saved through Faith in Jesus Christ as The Deliverer and Lord. This is accomplished in you ONLY by His Spirit first bringing you to contrition and repentance, then placing your faith solely in His Promise to be your redeemer, your Savior, your Lord of Life. When you do that He keeps His Promise to cleanse you from all unrighteousness and place His Spirit in you, right then, not after all that you can do to be worthy of His Grace.
Catholicism teaches a different means to be 'born from above', a means which looks more like an installment plan birth which requires your works to be completed. That is anathema to what The Word of God declares.
No lifetime of works is going to change an unrepentant heart, because ONLY God brings the sinner to the point of repenting and believing in Jesus as The Christ, The Son of the Living God. It is God's Holy Spirit Who brings the heart to the state of contrition that meets repentance.
This is as Catholics believe. Again, the Catechism of the Catholic Church:
1989 The first work of the grace of the Holy Spirit is conversion, effecting justification in accordance with Jesus' proclamation at the beginning of the Gospel: "Repent, for the kingdom of heaven is at hand." (Mt 4:17) Moved by grace, man turns toward God and away from sin, thus accepting forgiveness and righteousness from on high. "Justification is not only the remission of sins, but also the sanctification and renewal of the interior man. (Council of Trent (1547):DS1528)Pegs and 'whole' aside, the Bible very clearly and repeatedly tells you that it is by God's Grace that your are Saved through Faith in Jesus Christ as The Deliverer and Lord. This is accomplished in you ONLY by His Spirit first bringing you to contrition and repentance, then placing your faith solely in His Promise to be your redeemer, your Savior, your Lord of Life.
Agree, and very Catholic.
Catholicism teaches a different means to be 'born from above', a means which looks more like an installment plan birth which requires your works to be completed.
A false understanding of Catholicism. Works do not bring salvation, it is a pure gift through the merits of the sacrifice of Jesus on the Cross.
1992 Justification has been merited for us by the Passion of Christ who offered himself on the cross as a living victim, holy and pleasing to God, and whose blood has become the instrument of atonement for the sins of all men. Justification is conferred in Baptism, the sacrament of faith. It conforms us to the righteousness of God, who makes us inwardly just by the power of his mercy. Its purpose is the glory of God and of Christ, and the gift of eternal life: (Cf. Council of Trent (1547): DS 1529)Although frequently leveled by Protestants, the charge that Catholics believe in salvation through works is false. Where we do differ is that the reception of the Holy Spirit that comes with faith is progressive and not all at once. This is what we mean by an increase in Grace. It does not mean an increase in our own merit through our works. Nor does this need to be completed before death in order to earn Heaven. This cleansing of the soul is finished by God after death in Purgatory.But now the righteousness of God has been manifested apart from law, although the law and the prophets bear witness to it, the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: since all have sinned and fall short of the glory of God, they are justified by his grace as a gift, through the redemption which is in Christ Jesus, whom God put forward as an expiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins; it was to prove at the present time that he himself is righteous and that he justifies him who has faith in Jesus. (Rom 3:21-26)