Will a son be held accountable for remaining in his father's house, where his father feeds his family from the unlawful earnings of the lottery, given the son's inability to secure housing for himself or his mother?

The gambling-addicted father should be advised and warned of Allah's punishment with wisdom and good counsel. As for the family eating from his ill-gotten money, if all his money is unlawful, they are not permitted to eat from it if they are able to earn their own living. However, if they are not able to earn, then it is permissible for them to eat from it, as it becomes lawful for them. If he has both lawful and unlawful money, and the unlawful is more, then scholars have differed on the permissibility of eating from it.