Relfe v. Wilson was a United States Supreme Court case that dealt with the issue of whether a state court had the authority to issue a writ of habeas corpus to a prisoner who was being held in a federal prison. The case arose when a prisoner, William Relfe, was held in a federal prison in the state of Mississippi. Relfe sought a writ of habeas corpus from the state court, claiming that he was being held in violation of his constitutional rights. The state court granted the writ, and the federal government appealed the decision to the Supreme Court. The Supreme Court held that the state court did not have the authority to issue a writ of habeas corpus to a prisoner held in a federal prison. The Court reasoned that the writ of habeas corpus was a federal remedy, and that the state court did not have the power to interfere with the federal government's authority to imprison individuals. The Court also noted that the writ of habeas corpus was a remedy that could only be used to challenge the legality of a person's detention, and not to challenge the conditions of the detention. The Court's decision in Relfe v. Wilson established that state courts do not have the authority to issue writs of habeas corpus to prisoners held in federal prisons. This decision has been cited in numerous subsequent cases, and has been used to support the principle that state courts cannot interfere with the federal government's authority to imprison individuals.

In Relfe v. Wilson, the United States Supreme Court was tasked with determining whether a contract between two parties should be enforced when one of the parties had died before it could be executed. The majority opinion held that since there was no consideration for the agreement and both parties were not present to execute it, then the contract could not be enforced. Justice Field dissented from this decision, arguing that even though there was no consideration given for the agreement and only one party had signed it prior to death, an implied promise existed between them which should have been honored by enforcing their agreement in court. He argued that if a person enters into an arrangement with another individual who is deceased at time of execution or performance of said arrangement then they are still bound by its terms as long as they accepted those terms prior to death occurring; thus making enforcement possible despite lack of actual consideration being exchanged or both individuals being present at signing.