What is meant by :"they were believed to have lost in their long exile all national quality"?

What a wacko sentence!

Let's convert from a passive voice to an active voice: "People believed they had lost their national heritage in their long exile."

The tribes of Israel are the most notable groups that match that description. There are groups of people in S.E. Asia who don't know what a Jew is but they know they are Jews and one day they will be called back to their ancestral home, wherever that is. They truly have lost all national quality. The other tribes of Israel don't even remember that much.

Active voice: somebody does something
Passive voice: something is done - (by whom may or may not be emphasized)

"Avoid using the passive voice." - active - subject: you (imperative) - verb: avoid
"Use of the passive voice is to be avoided." - passive - subject: use or using (gerund) - verb: some form of to be