In Luke 15, in the case of the elder son, the father went outside the house and pleaded with him repeatedly; but the older boy would not yield. Jesus left the story open-ended at this point, leaving it to our imagination to decide what happened to him finally.
There are two possibilities: Either he may have yielded to his father's pleadings and finally come back home, with his head held high; or he may have rejected his father's pleadings and gone out into the darkness. Whichever way he may have chosen, he lost the place of honour in his home, for that had already been given to his younger brother. The father had already given his ring and the seat at his right hand to his younger son.
There is a vast difference between "prodigal sons" and "elder brothers". Prodigal sons are convinced of their sin on their own and repent deeply and seek no place of honour in the church. They only want to be slaves until the end of their lives. They are truly broken. "Elder sons", however, have to be repeatedly spoken to, before they are convinced. And even when they are convinced, they seek to come back to their place of honour in the church - as kings and not as slaves.
King Saul knew that he had sinned; but he wanted to confess his sin privately to Samuel. He told Samuel, "I have sinned; but please honour me now before the elders of my people and before Israel" (1 Sam.15:30). King David also sinned - far more seriously than Saul; but he wrote a psalm and acknowledged his sin publicly (Psalm 51).
Jesus told the Pharisees that their greatest sin was that they sought to justify themselves before men (Luke 16:15). God hates this sin more than any other. There is very little hope for a backslider who wants to justify himself before men.
God's word to sinners has always been: "Only acknowledge your sin" (Jer.3:13).
He who has ears to hear, let him hear.