My behaviour trees seem to still be active on AI death, I also added the AgentNolan behavior tree to my AI to see what would happen and it is the same, keeps seeking ammo when dead
I'm not part of the Opsive team, but you could just stop the BT when the character is dead. There's a node in actions called StopBehaviourTree, and you can also call it from a script. You could probably disable the component too.