In a multi-defendant federal case where judge has dismissed all but one federal claim and the federal claim goes to final judgment in plaintiff's favor and plaintiff appeals judge's decision to dismiss the state claims; what would happen with supplemental jurisdiction over those state claims?
It's hard to say for sure based only on the facts presented, but the appellate court likely would have jurisdiction to review the dismissal of the state-law claims. As one court has explained:
Pursuant to § 1367(a), when a plaintiff has alleged both federal and state claims, a district court may exercise supplemental jurisdiction over the state claims if they form "part of the same case or controversy" as the federal claim. In this case, the Plaintiffs' state claims plainly arise from the same "case or controversy" as the federal securities claim, for both the securities claim and the state claims arise from the same set of facts . . . . The district court therefore properly exercised supplemental jurisdiction over the state claims. And although the Plaintiffs have only appealed the dismissal of their state claims, the dismissal of those claims constitutes a "final decision" under 28 U.S.C. § 1291, and we therefore possess jurisdiction to resolve this appeal. See Groce v. Eli Lilly & Co., 193 F.3d 496, 502 (7th Cir. 1999) (reviewing merits of state claims where district court's jurisdiction derived from § 1367 and appellant only appealed state claims); Hamaker v. Ivy, 51 F.3d 108, 110 (8th Cir. 1995) (same).
Eriline Co. S.A. v. Johnson, 440 F.3d 648, 653 (4th Cir. 2006) (emphasis added).
The appellate court would have supplementary jurisdiction over the claims because the federal claim is still part of the case, if supplemental jurisdiction was appropriate to exercise over those claims because they arise from the "same nucleus of operative facts".
Since supplemental jurisdiction is a matter of subject matter jurisdiction, however, the existence of supplemental jurisdiction may be raised by any party at any time (even for the first time on appeal) or by the court sua sponte.
It could be that supplemental jurisdiction was present because there was a nucleus of common facts that pertained to a different federal claim than the one that was not dismissed. In that case, the supplemental jurisdiction might be lost of the state law claims lack a common nucleus of facts with the sole remaining federal claim (unless the dismissed federal claim is that related to the state law claim is also appealed).
For example, perhaps there were original federal claims and state claims related to a wrongful arrest, all of which were dismissed, and another federal claim relating to mistreatment while incarcerated after the arrest. In that case, the supplemental jurisdiction over the state law claims would be lost for purposes of the appeal unless the federal claim related to the arrest was also appealed. But, if the surviving federal claim was related to the arrest and the dismissed federal claim was related to incarceration after the arrest, then the supplemental jurisdiction would survive for appellate purposes.