Same thing that happens to any sinner. If he truly 'finds' (actually it is the Great Shepherd who does the 'finding') Jesus, he finds Him as Saviour and Lord. The sinner will want to please the Lord, and the Holy Spirit will help him overcome his sin. He may stumble along the way, but he will overcome. He will shed more or his sin nature and adopt more of the nature (imperfectly on this side of the grave - but to some degree) of his Lord.
1 John 3:2-9 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when He shall appear, we shall be like Him; for we shall see Him as he is. And every man that hath this hope in Him purifieth himself, even as He is pure. Whosoever committeth sin transgresseth also the law: for sin is the transgression of the law. And ye know that He was manifested to take away our sins; and in Him is no sin. Whosoever abideth in Him sinneth not: whosoever sinneth hath not seen Him, neither known Him. Little children, let no man deceive you: he that doeth righteousness is righteous, even as He is righteous. He that committeth sin is of the devil; for the devil sinneth from the beginning. For this purpose the Son of God was manifested, that He might destroy the works of the devil. Whosoever is born of God doth not commit sin; for His seed remaineth in him: and he cannot sin, because he is born of God.
Nicely phrased. All of us have weaknesses. For some, it is alcohol, for some, it is a desire to control the actions of others, and for some, it is an affinity for those of the same sex. For me, it is being too quick to anger. I have expressed that weakness here on FR, and have been wrong to do so. Like other weaknesses, the first necessary action is to admit the fault and then seek Christ’s help in overcoming it. Some weaknesses, like alcoholism, remain with a person all their earthly life. That doesn’t mean they should give in to those weaknesses. It just means their path is longer.