End of Evangelion and series spoilers
Asuka in End of Evangelion (EoE)
Asuka wakes up inside the entry plug of Evangelion unit-02 after being unconscious for quite some time, due to her many losses to the Angels and her drastic and fast downfall. Misato and the others had decided that while NERV was being attacked inside Unit-02's entry plug was the safest place there for her. She wakens after realizing what the AT field was, and just what EVA was to her. After awakening, Asuka attacks the JSSDF (Japanese Strategic Self Defense Force) which is attacking NERV, and while that occurs the MP (Mass Production Units 5-13) EVAs are headed straight for NERV. Asuka's power cord is cut and so that leaves Asuka with five minutes to destroy Evangelion units 5-13, giving her approx. 20 seconds per EVA. After pulling this off the Lance of Longinus comes from the sky and strikes Unit-02 in the head. Afterward the MP EVAs regenerate and attack unit-02, devouring it and ripping it to shreds. Afterward she is seen in some psychobabble scenes and then once again at the end, alone with Shinji by the ocean.
Does Asuka die in End of Evangelion?
My opinion. HELL NO! There are many reasons I believe this and the number one reason is just because the EVA dies does NOT mean the pilot is also dead. Many people who believe that she dies seem to be forgetting Genesis 0:9 episode 18. Evangelion Unit-03 was torn to SHREDS by Evangelion Unit-01, however Touji Suzahara was very much alive (unless you believe that it was all a big dream but then that would be unrealistic wouldn't it?). So that is the chief reason why I believe Asuka is NOT dead. The other is she probably wouldn't be able to come back at the end of EoE if she'd died...but that's just my opinion.