As a GM, you need to keep track of loose plot threads. But that doesn't necessarily mean you have to tie them all off neatly. Some can be left dangling. If players forget about them, that's not really a problem. That way you can either forget them yourself, or reactivate them later, reminding players that they forgot to take care of this one detail.
Commentary by memnarch (who has not seen the movie)
You know, I'd forgotten about this plot point as well. The brainwashing part that is; not the multi-identity man. I guess that means it's been long enough or there's been enough things happening between then and now that I'd have been got by Poe doing actually traitorous things.
I do like how obvious the GM is in wanting that particular plot wrinkle cleared up. So much so they didn't realize they were asking for Jim to go back to his usual style of roleplaying on a 3. Pete might be extremely good at character creation, but I don't think he'd have managed to succeed there without some more flaws being shared beforehand. Bad parking locations is only one point after all.
So are we wrapping up soon or something? I'm getting wrapping-up-the-movie-soon vibes from these conversations. If so, things feel a little unfinished, but Episode V did end on a similar note, so that's to be expected I suppose.
Transcript
Poe: I’ve got a loose end too!
Rey: Poe! Or is it Allan? Or Edgar?
Poe: That was part of it!
Poe: You all thought the identities were just a brilliant ploy to be accepted without suspicion after being brainwashed by Kylo Ren.
Rey: “Without suspicion”...
Poe: But I was riddled with conflict! I tried compartmentalising my mind into other personalities to outfox it.
Poe: It was going great until someone forced me to admit to being Poe again.
Poe: So I tried to sacrifice myself—heroically, of course—before I could betray the Resistance, but people kept stopping me. It’s like everyone wanted me to betray them.
Rey: So you’re still brainwashed?
GM: Oh, let’s not rehash—
Poe: Yeah! I mean...
Poe: Of course not, Rey! Why would you say such a thing?!
Rey: Can I Force Erase the brainwashing?
GM: Please.
Rey: I rolled a 3.
GM: Complete success! Poe is now free of Kylo’s control.
Poe: Phew! Now I can roleplay like I normally do again!
GM: Wait...