All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If what you meant is whether or not the sins of the singer will continue after his death because of people continuing to listen to his songs, then the answer is that it is confirmed that the Prophet said: "If anyone calls others to follow right guidance, his reward will be equivalent to those who follow him (in righteousness) without their reward being diminished in any respect, and if anyone invites others to follow error, his sin, will be equivalent to that of the people who follow him (in sinfulness) without their sins being diminished in any respect." [Muslim] So if the singer did not repent before his death, then it appears, Allaah Knows best, that every time the people would listen to his forbidden songs, then their sins will be added to his sins as he is the one who caused them to listen to his songs and made people sinful. Then his matter is in the Hands of Allaah, if He wants He will punish him and if He wants He will forgive him. The belief of Ahlus-Sunnah Wal-Jamaa'ah is that if someone dies while committing sins, he will be under Allaah's Will, Allaah may forgive him if He so wills, and He may punish him if He so wills.
Allaah Knows best.