Does severe illness that afflicted a deceased father alleviate the punishment for his sins, especially if he was a drug dealer, and what is the share of his children and wife in that, taking into consideration the almost non-existent income in Arab countries?

Consuming drugs is forbidden (haram), and money earned from drug trafficking is illicit. This illicit money does not become lawful for the heirs upon the death of its owner, according to the most preponderant opinion. Rather, they must spend it on general Muslim welfare or give it to the poor and needy. However, they may take from it what suffices their needs if they are poor. As for the father's condition after his death, the belief of Ahl al-Sunnah is that those who commit major sins are subject to Allah's will. Worldly tribulations may serve as expiations for sins, and there are other means of forgiveness, such as the intercession and prayers of believers, righteous deeds performed for the deceased, and the terrors of the grave and the Day of Judgment. Above all these is Allah's mercy and forgiveness for whomever He wills.