No, they think they are saved, no one knows who's saved only God. If you belong to God, the thing that you will be being saved from now is your sins, and you'll know this, because you should be overcoming them, you should be overcoming willful sinning and the lusts of the flesh, as the holy spirit shows you daily where your going wrong, and he'll be helping you to overcome if your heart is right before God.
As for eternal salvation no-one knows that only God. And Jesus taught us that we're to not to worry about tomorrow as tomorrow will take care of itself, there's enough trouble in the day we're in. I Just thank God that I'm blessed that he's given me food, drink and shelter and clothing and I'm blessed with a family, and I know that I'm to do what's right in my heart before him, and i leave my eternal salvation his hands.
If anyone believes that they can carry on living by the will of the flesh and they are still willfully sinning and God will be ok because Jesus had done it all for them, then they're badly mistaken. That's a false teaching from false churches!
We are being judged every day and we have Jesus as our example. God wants our heart right, and he wants us to deny sin, and this can only happen through Jesus he showed us the way and by the holy spirit who strengthens us.
And seeing as you only believe Paul
Titus 1
Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness; In hope of eternal life, which God, that cannot lie, promised before the world began
Romans 11
Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear:*For if God spared not the natural branches,*take heed*lest he also spare not thee.*Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in*his goodness: otherwise thou also shalt be cut off.