What does Paul grieving over the Corinthians imply? impurity, sexual sin and debauchery in which they have indulged.
  ourselves to you? We have been speaking in the sight of God as those in Christ; and everything we do, dear friends, is for your strengthening. 20 For I am afraid that when I come I may not find you as I want you to be, and you may not find me as you want me to be. I fear that there may be discord, jealousy, fits of rage, selfish ambition, slander, gossip, arrogance and disorder. 21 I am afraid that when I come again my God will humble me before you, and I will be grieved over many who have sinned earlier and have not repented of the impurity, sexual sin and debauchery in which they have indulged. - 2 Corinthians 12:19-21


In this passage Paul mentions that when he comes to the Corinthians again he fears that he would "be grieved" also those who have not repented of their sins. 

Does this imply Christians falling away from faith, sin resulting in death or is it a contextual issue?
In a sense, the issue is contextual. 

Repentance is not just for non-Christ followers; it is for everyone, Christians included. To repent is to do an about-face. You're going in one direction--the wrong direction, the carnal direction, as were some of the Corinthian believers--and you repent, make a 180-degree turn, and then go in the right direction. 

Let's say you're on a hike in some remote wilderness in the middle of nowhere. You ask a fellow hiker, "Where are the historic ruins of Kookamonga?" He tells you to go straight north about six miles, so you take off in the direction in which he pointed. 

A couple miles later you are not so sure you're going in the right direction. There were so many barriers preventing you from going straight north that you're actually now going south! Suddenly you remember there's a compass at the very bottom of your backpack, which you haven't used for years, so you take out your compass, get your bearings, and then go due north. You just repented. 

Some (most?) of the Corinthian believers were in need of repenting. God was grieved; so was Paul. He had labored hard among the Corinthian believers for many months, yet despite his labors and faithful teaching of the word of God, the believers were guilty of not just "impurity, sexual sin and debauchery" but also other sins:


disunity and divisiveness caused by a party spirit, such that splinter groups had formed around each group's favorite spiritual leader (1 Corinthians 1:12; cf. 3?4). Paul said in this regard, 



  What I mean is that each one of you says, “I belong to Paul,” or “I belong to Apollos,” or “I belong to Cephas,” or “I belong to Christ.” Is Christ divided? Paul wasn’t crucified for you, was he? Or were you in fact baptized in the name of Paul? (1 Corinthians 1:12-13; cf. 3:4).



taking fellow believers to court (1 Corinthians 6:1-7)
incest (1 Corinthians 5:1)
getting drunk at the celebration of the Lord's supper (1 Corinthians 11:20-21)


All this to say: Some of the Corinthians may have been living carnal, fleshly lives, but in Paul's letter to them he still addressed the believers as follows:


  From Paul, called to be an apostle of Christ Jesus by the will of God, and Sosthenes, our brother, to the church of God that is in Corinth, to those who are sanctified in Christ Jesus, and called to be saints, with all those in every place who call on the name of our Lord Jesus Christ, their Lord and ours. Grace and peace to you from God our Father and the Lord Jesus Christ! I always thank my God for you because of the grace of God that was given to you in Christ Jesus (I Corinthians 1:1-4 NASB, my emphasis).


Far from being Christians falling away from the faith, some of the Corinthians were not living up to the high moral and ethical standards to which they had been called in Christ. They were not part of the solution in immoral Corinth but were part of the problem. Instead of being salt and light, they were acting like pagans and participating in the works of darkness. 

No wonder Paul feared that God would humble him in their midst. Talk about "cognitive dissonance"! Paul knew that he had not only given the Corinthians sound, Spirit-filled teaching, but he also been provided them with a godly example as to how Christians should live (see 1 Corinthians 4:16; 11:1; cf. Philippians 4:9; 3:17; 2 Thessalonians 3:7-9).

Now he's hearing about all the carnality in evidence within the Corinthian church; he begins to wonder if he is somehow to blame; and he fears the Lord will humble him for perhaps thinking too highly of his teaching and his example. Perhaps he's even contemplating "leaving the ministry," as we might phrase it today. 

Paul's grief, then, is very real. At the same time, however, he realizes that the solution to the spiritual problems plaguing the church at Corinth requires thorough repentance, even if that means kicking some believers out of the fellowship of the saints until they come to their senses (see 1 Corinthians 5:9-13; cf. 1 Timothy 1:20). Yes, excommunication is a valid form of church discipline, but the goal must always be the restoration of the sinner to the Lord and then to the local body of believers. Here is what Gil Rugh has to say in this regard:


  . . . often . . . when a person is cut off from all association with believers . . .  the seriousness of the sin is recognized. The person may have nowhere to turn except back to God. If the person repents, the Church is to welcome the believer back immediately. Second Corinthians 2 says that the correct response is to immediately welcome the return of the believer. Thoughts of punishment and suffering are not appropriate. Remember, the goal is to restore, not to punish. As soon as the sin is acknowledged and left behind, the person is to be restored. That was the case in 2 Corinthians 2. "Sufficient for such a one is this punishment which was inflicted by the majority" (2 Cor. 2:6). Second Corinthians 2:7 continues the instruction, "So that on the contrary you should rather forgive and comfort him, lest somehow such a one be overwhelmed by excessive sorrow." There is no probation. After repenting from the sin, the believer is to be welcomed back. This is a manifestation of Christian love. "Wherefore I urge you to reaffirm your love for him. For to this end also I wrote that I might put you to the test, whether you are obedient in all things" (2 Cor. 2:8, 9). Paul continued, "But whom you forgive anything, I forgive also; for indeed what I have forgiven, if I have forgiven anything, I did it for your sakes in the presence of Christ, in order that no advantage be taken of us by Satan; for we are not ignorant of his schemes" (2 Cor. 2:10, 11). [my emphasis]


In conclusion, Christian discipline within any local body of believers is not optional but necessary. Without it, the testimony and reputation of the church are in danger of being compromised and besmirched. In Revelation, the apostle John was instructed by Jesus to write to the angel of the church in Ephesus the following warning:


  Therefore remember from where you have fallen, and repent and do the deeds you did at first; or else I am coming to you and will remove your lampstand out of its place—unless you repent (2:5 NASB).


Tragically a church can go down the tubes if loving discipline and genuine repentance are not in evidence.