first, even after the Kyuubi extraction, Kushina planned to seal the kyuubi back into her and die in order to gain some time. Imagine how much chakra she had even after the extraction.
second, she was planning to leave Minato with Naruto.
third, since they both quickly approached to save Naruto, plus she got herself stabbed as well even after she went through the extraction, Minato decided to seal her chakra inside Naruto (Minato knew that Kushina won't be able to survive both the damages at once)
OT: Why I believe Naruto won't die?
I made a prediction where it says (in short) Kurama gave up all the chakra (his own) to save Naruto. what left in Naruto is only Kurama's shell (just like Gedo Mazo) so that the chakra Naruto got from other tailed beasts will be fed into Kurama's shell along with Hachibi's tail and shukaku's chakra from Gaara. (No Kurama chakra from Minato yet)