Now if let's say someone stole it, will they stay in the PA until the Fusion Core runs out or until threat eliminated?
Fusion cores won't deplete on NPCs - if it's a settler, you can ask them to step out of the power armor, or if that topic doesn't show up simply remove the fusion core from their inventory. Otherwise, you can pickpocket it or shoot out the core, but those are easy ways to piss off, and possibly maim, whoever took your power armor.
I decided to test it. Put fusion cores in 6 PA suits and waited for an attack. 4 settlers decided to jump in PA. One of them left it after the fight. 3 others were walking in PA all day and only exited it before going to sleep. interesting thing is that they did not drain the cores at all. Cores stayed just as new. But I don`t know how it works with raiders or other npc.
You can also order a companion into a suit without a core and it will work normally for them. That was not the case a month or so ago.
I have been ordering my companions to use PA without cores since the game released.