Some thoughts:
We are saved by the finished work of Christ on our behalf. End of discussion. When a person repents "changes their mind" about their sin state, and their need for Christ, they are from that time forward born again. In the family of God. Our gracious, merciful God has made it that simple. We cannot front load OR back load the gospel with works. To front load it is to say we have to work to be saved, and to back load it is to say we have to do something to maintain or "prove" that we are saved. Any of this takes away from the gospel of Christ's FINISHED WORK ON THE CROSS. Simple.
Now about being apart of God's family. Now that we are in His family, there are some who choose to obey Jesus, and some choose not to. Simply put there are just things we as humans don't always want to give up. For some it might be sexual sin, for others it's overeating and for others it's gossip and being idle. We all know what our particular thing is that we either struggle with and in some cases give up the struggle and just give into. (it was noted that the Corinthians are a good example of brothers and sisters in Christ in this particular state.) God deals with His family about these matters. We've seen examples of people losing their lives due to sin they won't give up. These matters also have an effect on our reward at the Judgement Seat of Christ. If we are "living by the flesh" rather than "according to the Spirit" (and scripture makes clear we have a choice, proven by the fact that it has to be stated over and over to remind us of what we SHOULD do. If it was something we all would automatically do, it wouldn't have to be stated, urged and exhorted over and over to us.) The instructions about godly living is family business. Never meant to keep us always going back questioning our salvation, but always there to push us forward in becoming more like Christ so that when we stand before Him we are unashamed. Sanctification.
The foundation is SURE.

And only Jesus lays it down. I Cor 3:11 "For no one can lay a foundation other than that which is laid, which is Jesus Christ." Simple.
But about family matters: I Cor 3:12-15 "Now if anyone builds on the foundation with gold, silver, precious stones, wood, hay, straw- each one's work will become manifest, for the Day will disclose it, because it will be revealed by fire, and the fire will test what sort of work each one has done. If the work that anyone has built on the foundation survives, he will receive a reward. If anyone's work is burned up, he will suffer loss, though he himself will be saved, but only as through fire."
I want to ask a question to those of you who think someone "living in sin" who has also happened to put their trust in Christ's finished work, "was probably never saved" To those who think this, I have a logical question to ask...If you are talking to someone, say a Christian who continues to practice a sexual sin, and in your mind they must not be saved, but they attest that their confidence is in Christ's finished work for salvation.
How do you now witness to this person if you think they aren't saved, what gospel do you now share with them. They already believe in Jesus Christ, so in thinking they are not saved, how will you then try to convince them to be saved other than what they already believe? See...you'd have to change the gospel at this point. They already believe, scripture says this is the only means to justification, and yet you think they cannot possibly be saved because the way their life looks...what they are doing or not doing. There is no other gospel left other than what they already have put their faith in. This is why I think it would be more fruitful to exhort and encourage this brother/sister in Christ to godly living. Deal with them as a family member and show them what the scripture says. Don't bring into question their salvation for it was never Christ's intention for people to doubt His firm foundation. In fact Hebrews 5:11-6:3 makes it clear that anyone who keeps going over and over again the elementary teachings of Christ cannot move onto maturity. Hebrews 5:14 "But solid food is for the mature, for those who have their powers of discernment TRAINED by constant practice to DISTINGUISH GOOD FROM EVIL." and then Hebrews 6:1 says "THEREFORE (in light of what was just stated), let us leave the elementary doctrine of Christ and go on to maturity, not laying again a foundation of repentance......" Every time we doubt Christ's finished work it paralyzes us from being able to move onto maturity, and this is precisely where Satan wants us. Maturity by definition (Hebrews 5:14 IS distinguishing good from evil), this is why going around in circles about ones salvation can never produce fruit and a changed life. They remain infants. (and hence no wonder why they continue in sin because they aren't able to distinguish between good and evil.)
I would suggest that when we see one who calls himself a brother/sister in Christ in sin, we should simply do what the scripture says and : James 5:19 "My BROTHERS, if anyone among YOU wanders from the truth and someone brings him back, let him know that whoever brings back a sinner from his wandering will save his soul (life) from death (talking about physical death) and will cover a multitude of sins." This indicates that if we go after a brother who is living in sin, we might be able to even save their life. (they are already "saved" given the fact that we are talking about a "brother" specified by the scripture.) Recall that 1 John 5:16-17 states there is sin that leads to physical death. And note that "soul" and "life" are interchangeable. Not referring to "eternal life" but simply "life." As in: I almost got hit by a car and someone pushed me out of the way and "saved my life".
Galatians 6:1 "Brothers, if anyone is caught in any transgression, you who are spiritual should restore him in a spirit of gentleness. Keep watch on yourself, lest you too be tempted."
The matter of a brother /sister in Christ who is living in sin, is family business, not questioning the foundation laid by Christ Himself.