Some moral theorists argue that innocent beneficiaries of wrongdoing may have special remedial duties to address the hardships suffered by the victims of the wrongdoing. These arguments generally aim to simply motivate the idea that being a beneficiary can provide an independent ground for charging agents with remedial duties to the victims of wrongdoing. Consequently, they have neglected contexts in which it is implausible to charge beneficiaries with remedial duties to the victims of wrongdoing, thereby failing to explore the limits of the benefiting relation in detail. Our aim in this article is to identify a criterion to distinguish contexts in which innocent beneficiaries plausibly bear remedial duties to the victims of wrongdoing from those in which they do not. We argue that innocent beneficiaries incur special duties to the victims of wrongdoing if and only if receiving and retaining the benefits sustains wrongful harm. We develop this criterion by identifying and explicating two general modes of sustaining wrongful harm. We also show that our criterion offers a general explanation for why some innocent beneficiaries incur a special duty to the victims of wrongdoing while others do not. By sustaining wrongful harm, beneficiaries-with-duties contribute to wrongful harm, and we ordinarily have relatively stringent moral requirements against contributing to wrongful harm. On our account, innocently benefiting from wrongdoing _per se_ does not generate duties to the victims of wrongdoing. Rather, beneficiaries acquire such duties because their receipt and retention of the benefits of wrongdoing contribute to the persistence of the wrongful harm suffered by the victim. We conclude by showing that our proposed criterion also illuminates why there can be reasonable disagreement about whether beneficiaries have a duty to victims in some social contexts.