Bijuu aren't living beings like people or normal animals. They are living clusters of chakra. Yin Kurama wasn't dead. He was consumed by the reaper with Minato and when Orochimaru cutted shinigami's stomach he was released and incarnate in Minato's reanimated body because he was still his jinchuriki (the soul of bijuu and the soul of jinchuriki are connected).
I'm talking about biological aspect of they existence, no the psychological one. And yin Kurama wasn't dead.
He was sealed in Reaper's stomach with Minato's soul (because their chakra are connected like in other bijuu and jinchuriki case).