I might add that some Khazar statelets may have survived as long as 2 or centuries longer in the Crimea and the Caucasus. As for surviving Khazarian culture, the most romantic component, the Jewish adherence of the ruling and some of the merchant classes, dwindled with the end of Khazaria. It was a semi-nomadic Turkish culture with an overlay of cosmopolitan sophistication. The underlaying culture lived on in the myriad Turkish stepe tribes including the such as the Magyars.
Finally, the surviving documentation of Khazaria, especially in it's final period is so scant that it is hard to seperate fact from folktale.