Answer:
Two important examples of isolated languages are:
Basque: Basque is spoken by around 750,000 people in the Spanish Autonomous Community of Basque Country, and in the French department of Pyrenees-Atlantiques.
Basque is so isolated that it is a pre-Indo European language, and has survived over the years because the Basque Country is very mountainous, and because the Basque people have gone great leaps to protect it.
Korean: spoken by about 77 million people in both North Korea and South Korea, Korean is actually an isolated language because it does not have any close relations with any other language, or language family.
It has survived because Korea has been an important East Asian civilization since over one thousand years ago, and the prospect of this language is more positive than ever because of the increasing economic and cultural power of South Korea.