The scripture stated in 2 Corininthians 5:17 about the old being gone and new has come. It is saying that when someone gets saved and asks Jesus into their heart, a visible transformation takes place. If a visible transformation does not take place (not that we do it for show) then a person should really take the time and pray to God making sure their salvation and relationship is right with Him. Because what worries me about the person who made this statement to me has claimed they are saved, but I have known this person my whole life and there has not been evidence of transformation at all from what I can see. But it is not our place to play the role of the Holy Spirit; everyone must work out their own salvation.
I will tell you, though, the transformation is extremely evident in a person who was in a very dark place who lived in deep sin as I was at the time of my salvation. The evidence there is a bit more dramatic than others. I have a friend who was extremely sweet and soft spoken before she got saved and she is even sweeter after she got saved. So I do understand circumstances differ. But the transformational power of God is shined SO bright when a dark, lonley, filthy sinner runs home to Him.