Final answer:
Serbia was the country that remained united with Montenegro in the State Union of Serbia and Montenegro until Montenegro declared independence in 2006.
Step-by-step explanation:
The country that remained with Montenegro as the Federal Republic of Montenegro, until declaring independence in 2006, was Serbia. After the breakup of Yugoslavia, Serbia, and Montenegro were the only two republics that formed a union, officially known as the Federal Republic of Yugoslavia, which was later reconstituted as the State Union of Serbia and Montenegro before Montenegro's independence. This followed several years of political turmoil which saw the collapse of Communism in Eastern Europe and the subsequent disintegration of Yugoslavia. Montenegro, utilizing the euro as currency and focusing on privatization and tourism, finally became an independent state in June of 2006.