What is the ruling on buying a house from an elderly man, where the young man pays monthly installments for a specified period, and the house becomes the property of the young man upon the death of the elderly man, even if he dies a short time after the contract, knowing that the value of the house is predetermined and that the elderly man is non-Muslim and waives his right upon his death?

If the seller and buyer agree on an installment sale, the sale is valid. If the seller waives the debt during his lifetime or makes its waiver conditional on his death, it is permissible, because it is an absolution from one who is competent to dispose, and making the waiver conditional on the death of the waver is permissible by the consensus of jurists. The validity of a will from a disbeliever to a Muslim is permissible by the consensus of scholars. Likewise, it is permissible for the seller to stipulate the right to benefit from the sold house for a known period, such as inhabiting it until the installments are paid off or until his death, and the correct view is the permissibility of this condition.