What is an example of an individual displaying false repentance while claiming that he is truly repentant?

Jeff Pollard explains in this video that there was a young man who fell into the sin of fornication and was discovered in his sin. He came to the elders and made a confession of what he had been involved in. There were many tears and this man demonstrated extreme sorrow and anguish while he met with the elders of the church. There was a stated desire to walk with Christ and to honor him.

But, the evidence of his repentance, him breaking off his relationship with the girl, never happened. In time, it became clear that he was merely manifesting a worldly sorrow. He was sorrowful for the shame that he brought on his parents and sorry for the grief that he brought to his congregation, but it was all worldly sorrow. He was ultimately excommunicated and is still living in sin. Tears and words can be deceiving. 

Hebrews 10:29 (NKJV) – “Of how much worse punishment, do you suppose, will he be thought worthy who has trampled the Son of God underfoot, counted the blood of the covenant by which he was sanctified a common thing, and insulted the Spirit of grace?”

We had a young man who fell into the sin of fornication, was involved for many months in a heartbreaking relationship with the young woman behind his parents back. He was discovered in this sin and when he was discovered and came to the elders, he made a confession of what he had been involved in, of course he had been caught, but he made a full confession, he answered our questions. There were many many tears, we had several meetings with him, there were rivers of tears, sorrow, anguish, anger at himself, a desire, at least a professed desire to want to walk with Christ and to honor Christ. But the evidence of his repentance, breaking off the relationship with the young woman, never happened. And in time it became clear, not only to us, but even to him, that he was manifesting a worldly sorrow, sorry for all the trouble he'd caused, sorry for the shame that he brought upon his parents, sorry for the wounds and the grief that he brought to his congregation, and yet it was all worldly, fleshly.

He was excommunicated and is still in his sin. The remarkable thing about these two incidents is that the young man whose repentance was false was actually a more emotional, a more heart-rending, a seemingly more sincere sorrow and guilt over this particular sin, and yet it didn't break the pattern of the sin. In the other man, it had been perhaps a bit more staid, did not have the outward rivers of tears that we had with the young man, there was a clear and palpable change in the relationship between him and his wife and even in his reactions and interactions with the congregation after that. So there was clearly a change in this man's life as opposed to the young man's life who has to this day not broken that pattern of sin.