We know that the ruling elite and many other people of the Khazars have converted to Rabbinic Judaism. What happened to these people after the fall of the Khazar state? Why did they disappear?
Khazaria was multi ethnic state whose focus to facilitate international commerce through transcaucasus and the Pontic steppe region. Its core was composed primarily of a Turkic, or Turco-Iranian, and Slavic component. The Slavs remained in the region and became considerable part of the Rus. Khazaria also ruled over numerous other subject peoples, mostly Turkic. The decline of Khazaria was a tumultuous time in the entire steppe, as waves of Oghuz and Pecheng turks continuously pressed west and displaced others. The successors to the Khazars became the Rus in the west, and the Pechengs in the east. As mentioned, the Rus had absorbed the slavic component of Khazaria, the Pechengs were altogether new invaders, but also Turkic.
The decline of Khazaria began around 830. There was a civil war around this time that was started by a group called the Qabars, which means rebel in Old Turkic. The Qabars were defeated, and joined the Hungarians in their settlement of Hungary. Also around this time, the Rus Khaganate was formed to the Northwest. Exactly why they had a Khagan, and the extent to which it was influenced by Khazaria, is disputed.
Seljuk began his career as an officer in the Khazar army. The names of his sons suggests he was a Khazar Jew. He adopted his grandon Tugril, who founded the Seljuk Empire.