Praise be to Allah.
There is no sin on the children of one who deals in riba even if he spends purely riba-derived money on their food, clothes or travel, if they have no other way of earning a living. They have to advise their father in the manner which they think will be most effective. If it is easy to find other means of earning a living, or they do not need that money for the essentials of living, then they have to do without it.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
If the father’s earnings are haram, then it is essential to advise him. Either you can advise him yourselves, if you are able to do that, or you can seek the help of scholars who can convince him or of his friends who may be able to convince him to avoid these haram earnings. But if that is not possible then you may benefit from it as much as is necessary, and there is no sin on you in this case, but you should not take more than you need because of doubts as to whether it is permissible to benefit from one whose earnings are haram.
(Fatawa Islamiyyah, 3/452).
If a father who deals in riba dies, his heirs must get rid of the riba-based money by returning it to its owners if they are known. Otherwise they should get rid of it by spending it in charity, whether that is given individuals or to institutions. If it is too difficult for them to find out exactly how much of their father’s wealth is riba-based, they should divide it in half, taking one half and distributing the other half.
Shaykh al-Islam Ibn Taymiyah was asked about a man who dealt in riba, and who left behind wealth and a son who knew his father’s situation – was the wealth permissible for the son as inheritance or not?
He replied: with regard to the amount that the son knows is riba-based, he should get rid of it, either by returning it to its owners if possible, and he should not give it in charity. The rest is not haram for him. With regard to the amount concerning which there is doubt, it is mustahabb for him not to take it unless it is needed to pay off a debt or to spend on dependents. If the father died when engaging in riba-based transactions that are allowed by some fuqaha’, it is permissible for the heir to benefit from them. If the halal and haram are mixed and the extent of each is unknown, it should be divided into two halves.
(Majmoo’ al-Fatawa, 29/307).
And Allah knows best.