Yes, unfortunately, Kurama passed away in the manga. This occurrence brought about a lot of changes and emotions for both the characters and the readers.
Kurama might become angry at first. He's a powerful being and being neglected would likely wound his pride. He could start causing some minor disruptions inside Naruto, like making it harder for Naruto to access his chakra.
Well, Kurama might train Naruto by teaching him how to better control and access chakra. Since Kurama has a vast amount of chakra, it could show Naruto unique ways to harness and use it. For example, it could guide Naruto in creating more powerful and complex jutsu by using their combined chakra in a more efficient way.
Kurama makes a comeback in the manga. The return is well-plotted and adds an interesting twist to the story. It also ties up some loose ends and brings new possibilities.