Objection 1. It would seem that an indulgence avails those who are in mortal sin. For one person can merit grace and many other good things for another, even though he be in mortal sin. Now indulgences derive their efficacy from the application of the saints' merits to an individual. Therefore they are effective in one who is in mortal sin.
Objection 2. Further, the greater the need, the more room there is for pity. Now a man who is in mortal sin is in very great need. Therefore all the more should pity be extended to him by indulgence.
On the contrary, A dead member receives no inflow from the other members that are living. But one who is in mortal sin, is like a dead member. Therefore he receives no inflow, through indulgences, from the merits of living members.
I answer that, Some hold that indulgences avail those even who are in mortal sin, for the acquiring of grace, but not for the remission of their punishment, since none can be freed from punishment who is not yet freed from guilt. For he who has not yet been reached by God's operation unto the remission of guilt, cannot receive the remission of his punishment from the minister of the Church neither by indulgences nor in the tribunal of Penance.
But this opinion seems to be untrue. Because, although those merits which are applied by means of an indulgence, might possibly avail a person so that he could merit grace (by way of congruity and impetration), yet it is not for this reason that they are applied, but for the remission of punishment. Hence they do not avail those who are in mortal sin, and consequently, true contrition and confession are demanded as conditions for gaining all indulgences. If however the merits were applied by such a form as this: "I grant you a share in the merits of the whole Church--or of one congregation, or of one specified person," then they might avail a person in mortal sin so that he could merit something, as the foregoing opinion holds.
This suffices for the Reply to the First Objection.
Reply to Objection 2. Although he who is in mortal sin is in greater need of help, yet he is less capable of receiving it.
Source: Summa Theologica (New Advent)