Here's my prediction:
I think Shiida is clearly being set up, but we don't know how much she knows - she was late to the party regarding knowing that Iruma is human, after all, so it's very possible that she doesn't know that say, her recommendation to Babyls as a teacher was from a guy with ties to Border Patrol (Narnia).
However, the teachers (at the very least, Balam, Kalego, and Opera) know that Atori and Shiida were recommended through Narnia - and may be every bit as apprehensive about sending her to Border Control custody as they were when making plans for Shiida to return to teaching under supervision back during the aftermath of Heartbreaker.
Shiida currently seems to be operating the assumption that her goal right now is to protect Iruma, the human, from Border Control. Based on Iruma's respective impressions on Fenrir and his platoon from Border Control and Shiida, Iruma will likely take Shiida's side of the fight.
Iruma backing Shiida means they last long enough against Fenrir for a teacher - likely Kalego imo, to reach the roof to investigate the disturbance, and while I'm not sure of the specifics (if Kalego and Fenrir/Narnia throw down here), I think Shiida will ultimately suspect some sort of setup after hearing new information about her situation and throw a wrench in the setup plan by offering to surrender to Babyls, rather than Border Control. Based on Fenrir's opening shot, the way she was deceived, and her teaching sponsor - Narnia - having ties to Border Control, imo she could reach that conclusion fairly quickly with the right information, info that Kalego could provide.
It would lead to a jurisdictional dispute between multiple 13 crowns (Narnia, Henri, Sullivan, possibly Baal, Bachiko, Mephisto), and Henri in particular will probably have to make a difficult decision considering how his human sympathies and likely knowledge of Narnia's tendencies will likely clash with his leading role in Border Patrol.
It could also lead to a broadening of the knowledge that Iruma is human, and while I don't think he gets fully outed (I think that's a whole separate major arc further down the line) imo it's likely the info reaches to more of the teaching staff and leads to a lot more awkwardness.