The IRS says my client, who has lived in Italy for the last 15 years, still owes the taxes they owed when they moved to Italy. We have been fighting with them because the ten-year Collection Statute has expired. Do you have any advice?

Unfortunately the IRS is correct. One of the collection statute tolling events (an event that stops it from running) is being outside the United States for more than six months. It is why the IRS asks this question on the Form 433. Hence your client just tolled the statute and if the taxes were within the Collection Statute Expiration date when they left the US those taxes are almost certainly still in the same place now and are still owed.