Complex sentence: The Azerbaijanis in Armenia were the largest ethnic minority, but have been virtually non-existent since in 1988--1991 when most Azerbaijanis fled the country as a result of the Nagorno-Karabakh War and the ongoing conflict between Armenia and Azerbaijan.
Split into simpler sentences: The Azerbaijanis in Armenia represented a large number but have been virtually non-existent since in 1988--1991. Most Azerbaijanis fled the country as a result of the Nagorno-Karabakh War and the ongoing conflict between Armenia and Azerbaijan.