Restitution is prescribed by Yahweh in the Torah for specific offenses like nonlethal assault without permanent injury (Exodus 21:18-19, 22), theft (Exodus 22:1, 4-9, Leviticus 6:1-5, and Numbers 5:5-7 as will be discussed below), and accidentally eating sacred offerings meant for the Levitical priests (Leviticus 22:14-16). As there is no longer a Levitical priesthood, this particular obligation could not possibly exist anymore, but the rest can and do according to the Bible (Matthew 5:17-19, for instance). The nature of restitution along with the sometimes greater repayments mandated in the Bible is the following: it is to give back the lost item or money/something of equal value or make up for harm or lost labor (Exodus 21:18-19) and, when applicable, punish the wrongdoer beyond rectifying the initial misdeed.
When Exodus 22:1 and 4 give different ratios for repayment of stolen animals, the factors of the theft are the reason. In the first case (22:1), that of someone stealing an animal which is then killed or sold, the owner has little chance or none whatsoever of reclaiming it. The penalty is thus greater because the impact of the loss is greater or more lasting. The thief accordingly has to replace the animal and then provide several more. In the second case (22:4), the stolen animal is found alive in the possession of the thief, and they only have to pay back double. Here, the very animal that was taken can still be restored to the owner as a pet or creature of labor, so the punitive aspect of the restitution—adding a second animal—is smaller than the ratio of three or four additional animals in verse 1.
What, though, of an instance where the victim has died after the offense, yet before the offender tries to repay them? A passage from Exodus 21 addresses this to some extent in its commands regarding a negligent owner of an animal that kills someone, despite how the very nature of this sin actually leads to the victim's life being extinguished so that they cannot receive anything as payment.
Exodus 21:28-30—"'If a bull gores a man or woman to death, the bull is to be stoned to death, and its meat must not be eaten. If, however, the bull has had the habit of goring and the owner has been warned but has not kept it penned up and it kills a man or a woman, the bull is to be stoned and its owner also is to be put to death. However, if payment is demanded, the owner may redeem his life by the payment of whatever is demanded.'"
Obviously, if a person is killed by a habitually dangerous animal, they are no longer alive to receive compensation for any injury; he or she is dead. Thus, though the owner of the bull is permitted to give money or property to deliver themself from the otherwise deserved death penalty (as opposed to cases of murder according to Numbers 35:3-31), the victim is not the person whom this restitution would go to. It would be impossible. The next closest person would be some sort of immediate family member, a parent or sibling or spouse, and then an extended family member, such as a grandparent or grandchild. In the absence of any family members, perhaps payment could be made to the governing body, yet this is not the norm in Biblical prescriptions. The default for restitution is that the victimized man or woman is the one compensated (once again, see Exodus 21:18-19, 22:1, 4-9, and so on).
There is another example which all but directly states that family members receive restitution if the victim dies or is unavailable:
Numbers 5:5-8—"The Lord said to Moses, 'Say to the Israelites: "Any man or woman who wrongs another in any way and so is unfaithful to the Lord is guilty and must confess the sin they have committed. They must make full restitution for the wrong they have done, add a fifth of the value to it and give it all to the person they have wronged. But if that person has no close relative to whom restitution can be made for the wrong, the restitution belongs to the Lord and must be given to the priest, along with the ram with which atonement is made for the wrongdoer."'"
This passage echoes the restitution plus additional payment of one-fifth of the value introduced in Leviticus 5:14-16 and 6:1-5, assigned in the latter specifically to matters of theft by deception or the selfish keeping of lost property. Again, the base restitution is to return the lost item, replace it, or make up for its value, and in this and other restitution passages, any additional compensation (whether in the form of an animal or money) is the strictly punitive element. In the context of Leviticus 6:1-5, this is not applicable to cases of assault without permanent injury, which have their own separate ranges of payment. Now, Numbers 5 goes from prescribing compensation to the victim of the offense, and then it shifts to what to do when there is no close relative to repay. The unspoken but logically required concept is that the victim would be unable to receive restitution, likely because they are not alive anymore. In the absence of a living victim to make amends with, the payment next defaults to immediate family members, and then to God or his priestly representatives when the sons of Aaron were still active in their roles.