More recently, it was confirmed in the Boruto series that after Kurama died, he reincarnated in the ninja world. Reincarnation is apparently random and can happen at any point and any place.

Naruto's Pilot Made Kurama His Father As Opposed to the Fourth ... Naruto is not only the Fourth Hokage's son, but is also the reincarnation of Asura, Naruto establishes that heroism, kindness ...