The Khazars like many steppe empires where in regular contact with the settled societys. I is very common that start adopting or adding other religions. The Khazar case is not really all that special exept that the ruling elite prefered judaism. However it is wrong to assume that all Khazars were Jews, more likly Jews where a minority compared to muslims and chritians.

The Khazars where very good with economic development. The made live easy for merchants and profited from it. Many merchants where jews and that where the came in contact with it. However I do not know if the jews sent in people specificly to convert Khazars. The christians defently did so.

They, like most steppe empires, got destroyed eventually by other steppe people coming from the east. Wars with the Roman Empire probebly cost them a lot of resources and power, and eventually they broke under the pressures.

However the individuals and even tribes probebly did not get wiped out, they where now just attached to another steppe confedaration.