What is the ruling of Islamic law regarding how to deal with a person who regrets having committed sodomy, suffers from physical and psychological illnesses as a result, believes his punishment is death, and asks about the permissibility of suicide to end his suffering and prevent disgrace to his family?

Sodomy is a grave indecency, and the punishment for its perpetrator is death. However, it is not obligatory for the perpetrator to confess their crime; rather, it is better for them to repent and conceal themselves with God's concealment. Suicide is a grave crime whose doer is threatened with Hellfire, and your friend must avoid this thought. The execution of capital punishments is the prerogative of the ruler or their deputy. Repentance is sufficient, for it expiates what precedes it. Your friend must know that the punishment of this world is not comparable to the torment of the Hereafter if they commit suicide.