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Italy and the United States have an extradition treaty, which means that, upon request, America is theoretically obliged to surrender fugitives who have been convicted of crimes in Italy, and vice versa. In practice, there are exceptions to the rule. Countries can and do deny extradition requests for many reasons: if the accused will be subject to double jeopardy; if extradition is requested for political or military offenses; if the would-be extraditee is powerful and famous.
I predict that, even if she is convicted in absentia, theres no way that Knox will be extradited back to Italy to serve her sentence. Knox is a cause célèbre in the U.S., and her partisans will exert significant pressure on the government to deny any extradition request. Article X of the current U.S.-Italy extradition treaty states that the requesting nation must present a case summary that provides a reasonable basis to believe that the person sought committed the offense for which extradition is requested. The United States will probably use this as grounds for blocking Knoxs extradition. They might cite double jeopardy, too, but thats a trickier argument to win under the current treaty.
More likely is that, if Knox is convicted again, Italy wont even bother requesting her extradition. Doing so would cause a small but real international incident, something that both nations would prefer to avoid. The two countries will reach some sort of agreement, and Knox will never spend another day in an Italian jail.