Emperors Theodosius II and Valentinian III eliminate any statute of limitations when it comes to investigating apostates' wills. Apostates aren't allowed to give testaments and their goods can only be willed to close relatives.
According to this law:
"The investigation of apostasy will not be prevented by any time limitations. Because they have deviated from the faith, they must have no power to make a testament or gift, nor can they defraud the law by the pretense of a sale. On intestacy [dying without a will] all their property must go to near kinsmen, preferably Christians.
Taking action against such sacrilege requires that when anyone who receives an inheritance on intestacy, there will be an unrestricted right of due accusation, even after the death of the sinner. To prevent the crime from being interpreted too broadly, though, We will only pursue those who have made sacrifices after converting to Christianity.
The proved perfidy of such people will be punished by having their gifts and testaments rescinded and their inheritances will be given to heirs who are stipulated by the law." [CTh 16.7.7]
This prevents apostates from passing their property along to other apostates and thereby improving the social and financial status of apostates generally. Apostates who are close relatives may still benefit, but relatives who are orthodox Christians will be preferred if there is any choice.