Objection 1. It would seem that there remains no debt of punishment after sin. For if the cause be removed the effect is removed. But sin is the cause of the debt of punishment. Therefore, when the sin is removed, the debt of punishment ceases also.
Objection 2. Further, sin is removed by man returning to virtue. Now a virtuous man deserves, not punishment, but reward. Therefore, when sin is removed, the debt of punishment no longer remains.
Objection 3. Further, "Punishments are a kind of medicine" (Ethic. ii, 3). But a man is not given medicine after being cured of his disease. Therefore, when sin is removed the debt of punishment does not remain.
On the contrary, It is written (2 Samuel 12:13-14): "David said to Nathan: I have sinned against the Lord. And Nathan said to David: The Lord also hath taken away thy sin; thou shalt not die. Nevertheless because thou hast given occasion to the enemies of the Lord to blaspheme... the child that is born to thee shall die." Therefore a man is punished by God even after his sin is forgiven: and so the debt of punishment remains, when the sin has been removed.
I answer that, Two things may be considered in sin: the guilty act, and the consequent stain. Now it is evident that in all actual sins, when the act of sin has ceased, the guilt remains; because the act of sin makes man deserving of punishment, in so far as he transgresses the order of Divine justice, to which he cannot return except he pay some sort of penal compensation, which restores him to the equality of justice; so that, according to the order of Divine justice, he who has been too indulgent to his will, by transgressing God's commandments, suffers, either willingly or unwillingly, something contrary to what he would wish. This restoration of the equality of justice by penal compensation is also to be observed in injuries done to one's fellow men. Consequently it is evident that when the sinful or injurious act has ceased there still remains the debt of punishment.
But if we speak of the removal of sin as to the stain, it is evident that the stain of sin cannot be removed from the soul, without the soul being united to God, since it was through being separated from Him that it suffered the loss of its brightness, in which the stain consists, as stated above (Question 86, Article 1). Now man is united to God by his will. Wherefore the stain of sin cannot be removed from man, unless his will accept the order of Divine justice, that is to say, unless either of his own accord he take upon himself the punishment of his past sin, or bear patiently the punishment which God inflicts on him; and in both ways punishment avails for satisfaction. Now when punishment is satisfactory, it loses somewhat of the nature of punishment: for the nature of punishment is to be against the will; and although satisfactory punishment, absolutely speaking, is against the will, nevertheless in this particular case and for this particular purpose, it is voluntary. Consequently it is voluntary simply, but involuntary in a certain respect, as we have explained when speaking of the voluntary and the involuntary (6, 6). We must, therefore, say that, when the stain of sin has been removed, there may remain a debt of punishment, not indeed of punishment simply, but of satisfactory punishment.
Reply to Objection 1. Just as after the act of sin has ceased, the stain remains, as stated above (Question 86, Article 2), so the debt of punishment also can remain. But when the stain has been removed, the debt of punishment does not remain in the same way, as stated.
Reply to Objection 2. The virtuous man does not deserve punishment simply, but he may deserve it as satisfactory: because his very virtue demands that he should do satisfaction for his offenses against God or man.
Reply to Objection 3. When the stain is removed, the wound of sin is healed as regards the will. But punishment is still requisite in order that the other powers of the soul be healed, since they were so disordered by the sin committed, so that, to wit, the disorder may be remedied by the contrary of that which caused it. Moreover punishment is requisite in order to restore the equality of justice, and to remove the scandal given to others, so that those who were scandalized at the sin many be edified by the punishment, as may be seen in the example of David quoted above.
Source: Summa Theologica (New Advent)