J just started my first char to test these things. As far as i know when you die in your fraction headquarters, you can't lose items. But if you attack on your people, every npc will try to kill you ASAP. You also lose reputation for backstabbing, either its npc or player. Below 10000 reputation (you start with this amount) fraction kicks you out. (You can't enter the big building).
If you die in the core, or in the wasteland, you lose all of your items and you respawn at the last of your fraction HQ, even if you are no longer have permission to enter.
Correct me if im wrong.