I tested yesterday with a group member, I used regular Naruto for testing, he was skillbooked, but he has no scaling skills, and I used Kushina of course. After Kushina died, Naruto was dealing ~830 damage with his standard, after the next mystery launched or two, his standard was dealing ~870 damage, and it was long after Kushina was already dead. So I think the scaling of the Kushina Christmas passive, when ninja consumes chakra, stays in effect after her death.

The effect does not freeze when she is dead, meaning that the % buff you gained before she died, is not staying at that %, but instead keeps increasing after her death every time your specific ninja consumes chakra.