Yes, God can forgive a soul in Hell when they ask for pardon. But..
Question: Can God forgive a soul in Hell when they ask for pardon?
Answer: Emm, Yes
However there is a “But". Let’s get something straight first, NO SOUL IN HELL CAN BE SAVED. This does not mean that God cannot forgive a soul in hell when they ask for pardon, it means however that the soul CAN NO LONGER ASK for pardon from God from a sincere heart. Souls in hell cannot love, cannot be sorry, cannot be moved to anything good and sincere, therefore, they cannot be moved to speak to God in a loving manner.
When this soul was on earth it didn’t want communion with God, it resisted the graces of God; it wanted to be “left alone". Hell means a state of “being left alone" for all eternity.
God respects everyone’s free choice to be left alone. He can NEVER COERCE; he can never force anyone to commune with him in Heaven when they don’t want it. “Wanting it" means obeying God’s commands till the end, using the Sacraments worthily, paying an ear of obedience to the Church. Sin means refusing God either temporarily or permanently when we sin and refuse to abandon those sins and return to Him.
“We cannot be united with God unless we freely choose to love him. But we cannot love God if we sin gravely against him, against our neighbor or against ourselves: “He who does not love remains in death. .. To die in mortal sin without repenting and accepting God’s merciful love means remaining separated from him for ever by our own free choice. This state of definitive self-exclusion from communion with God and the blessed is called “hell.””
– CCC 1033
God NEVER changes, He is ALWAYS merciful. However, the souls in hell are selfish and against God. They HATE His Light, His Name, His Face and everything about Him to them breeds hatred and disgust. That’s “Hell"; they are forever cut off from the most Beautiful, Powerful, Loving, Peaceful Father and Lover. A soul in hell does not have the light of grace to feel contrition. In fact so many Church Fathers believe that the souls in hell curse and rant against God for all eternity.
Is this surprising? A soul who rebelled against God in life cannot be his friend in death. This soul has so disposed himself to selfishness and self-love that he is absolutely unable to love God or any other except himself. In fact, at death, he is also unable to love himself since true self-love ultimately comes from God. One can say that a soul who loved himself in life necessarily does anything to ensure his happiness for all eternity.