God's grace (undeserved, unmerited, unearned favor) empowers us to experience victory over sin, unclean habits and addictions in our lives. In other words, God's grace gives us dominion over sin (Romans 6:14), NOT keeps us under the bondage and power of sin.
The Bible is very clear, and emphatic, about this. Romans 6:14 says, "For sin shall not have dominion over you, for you are not under law but under grace." Sin loses its control ("dominion") over you when you are under grace ("not under law but under grace").
In the story of the woman caught in adultery, the Bible records Jesus telling her, "Neither do I condemn you; go and sin no more." (John 8:10–11) Jesus extended His grace (undeserved, unmerited, unearned favor) to the woman by giving her the gift of no condemnation first, and in doing so, He empowered her to "go and sin no more". He did this because He knew that He would bear her sins on the cross. So, it is only when someone truly has a revelation that God does not condemn them, because of what happened at the cross, that they would have the power to get out of the vicious circle of sin.
In the Gospels, Jesus plainly taught that if someone understands how much God has forgiven them through the finished work of Christ, he or she would fall in love with Jesus and love Him even more (Luke 7:47, New Living Translation), not go out and sin more, or go on living in sin.
So, if someone says, "Well, I am under grace," but continues to live a lifestyle of sin, this person does not understand grace at all. Again, the Bible says in Romans 6:14 that "sin shall not have dominion over you, for [or because] you are not under law but under grace". So, the person may say he is under grace, but he is not enjoying the gift of no condemnation nor is he enjoying the free, unmerited favor of God. That is why sin still has dominion over him.
Someone who has really known and experienced grace and the gift of no condemnation will NOT want to live in sin. Sin will be the last thing on his mind. A person cannot claim to be under grace when he/she continues to live in sin because grace ALWAYS results in victory over sin.