What happened to Kushina's soul During the 9 tails attack on the hidden leaf, Minato along with Kushina performed the death reaper sealing jutsu and sealed the Kyuubi into Naruto. Its been known that those who perform this forbidden sealing jutsu sacrifice both their lives and souls to the death reaper. However, Minato said he would also seal part of Kushina inside Naruto (which he actually did). 

Does this mean that half of Kushina's soul was sealed in Naruto while the death reaper took the remaining half? Or were both hers and Minato's taken by the death reaper.
Nothing special happened to Kushina's soul, she died from having Kurama extracted from her body and the wounds inflicted during the battle with Kurama.

Minato used the Death Reaper on himself to seal away the half of Kurama that he had stored in himself. The other half got sealed in Naruto and Minato infused the Eight Trigrams Sealing jutsu with his own and Kushina's chakra.

Here you can find the scene where Kushina tells Naruto that Minato had infused her chakra into the seal: https://youtu.be/D3tJoGr6pp4?t=68