While some believe that Khazaria was diminished by the 10th century, archeological and historical evidence show that the Empire continued to flourish until the 13th Century and that it was the Rus, not the Mongols who ruined Khazaria. The Rus were not alone, they were assisted by the Black Death, thought to have started in China, it travelled along the Silk Road through Khazaria until and reached the Crimea by 1346. While reports of the death count in Eurasia are scarce, we can assume that the death toll was as high as in Europe, that is 1/3-2/3.
What did the Khazars do against these strikes from the north and the east? They could not run south, because they were not on good terms with the Shadow Caliphate, to say the least. On the other hand, they had many colonies on the east in countries like Hungary, Romania, and Kiev.
Did they make it there in time? How many made it? Koestler estimated the number of the newcomers in half a million. What did they look like genetically? What about the populations who did not complete their conversion to Judaism? Were they perished, accepted among the Jewish communities, or did they survive in small communities watching their Empire burn to the ground?
We hope to be able to answer at least some of these questions.
Our secondary goal is to develop a test to find the Khazar descendants.