From the Summary: "Restitution in federal criminal cases is a matter of statute. A handful of statutes identify the victims who are eligible to receive restitution; what criminal convictions may trigger an obligation to pay restitution; the losses for which victims may be compensated; and the procedure by which restitution is ordered and enforced. [...] The Department of Justice, acting on behalf of a victim, may enforce a restitution order in the manner it uses to collect fines or by 'all other available and reasonable means.' Victims may secure a lien in their own names against the defendant's property in order to secure restitution, and they may bring other civil actions in their own names against the defendant. The courts do not agree on whether the abatement doctrine cuts off unfulfilled obligations under a restitution order. The abatement doctrine provides that when a defendant dies while his or her appeal is still pending the law treats the defendant's indictment and conviction as though they had never happened. The conviction is vacated and the indictment dismissed."
CRS Report for Congress, RL34138
Congressional Research Service: https://crsreports.congress.gov/