Tory v. Cochran
In Tory v. Cochran, 544 U.S. 734 (2005), the U.S. Supreme Court implied that a permanent injunction may in rare circumstances be a constitutional remedy in a defamation action, even to the extent of preventing all future speech about an admitted public figure. In other words, the First Amendment does not automatically prohibit all permanent injunctions against this type of speech.
However, the Court did not expressly hold that. Because Johnnie Cochran had recently passed away, the "injunction-forbidden speech could no longer achieve the objectives that the trial court had in mind (i.e., coercing Cochran to pay a "tribute" for desisting in this activity)." Accordingly, "the grounds for the injunction are much diminished, if they have not disappeared altogether. Consequently the injunction, as written, now amounts to an overly broad prior restraint upon speech, lacking plausible justification."