Carme's lungs do not work right. They never have. She gets sicker when she spends time in bad air. She usually spends all winter barely able to shuffle to work, write diagrams on the board, hiss incantations under her breath, snap her fingers at malingering students, and shuffle home again to curl up next to a steaming teakettle. She was obviously too fragile to be of use at the Worldwound, so she paid her debts by remaining at school, forever.
There's nothing quite like mortal peril to focus the mind on spellcraft. But if there is a second place to be had, after mortal peril, it is huddling under your blankets, recasting a Light over and over on a long wand that can illuminate the page before you without you having to stick a fingertip out into the cold of your unheated dormitory. It is lacking the breath and the endurance and the energy to go out dancing with your friends, or to have friends in the first place. It is looking like an ill, distracted woman walking alone and leaning against a wall to cough, until a pickpocket meets the business end of your viper familiar.
("Can't she hang Endure Elements?" people ask. She eventually can: she can hang it and cast it and feel her fingers again; she can hang it and cast it and her cheeks will stop flushing - but the problem is the lungs, the problem is the dryness in the air, smoke from hearths, miasma from the stinking bay and horse manure in the streets. A squishy wizard indeed, is Carme.)
So she can't do much but study. So she studies. She can teach the theory on spells all the way up to fourth circle, for all that she can only hang a single third circle specialty-school conjuration on a good day. She tutors, her snake Myrtle coiled around her neck in patient threat if anyone should take her wheezing as a temptation to strike her. And she teaches, mostly Conjuration but she can substitute for most of the others.
When the war comes, she simply stays home. She never told anybody she'd hold a position in the damn place and defend it against invasion. They all know she's not suitable for a fight anyway. And when it's over, she goes right back, like nothing happened except for the Evocation lecturer taking a leave of absence. Indefinitely. In Hell. But the little squirts still need to be trained to sit still and focus, to draw neatly and multiply accurately. In she goes, every day.
Someone is supposed to be a representative to the Constitutional Convention. The Divination teacher and the Transmutation teacher hate each other and the headmaster's bitter about the war and the Abjuration teacher literally can't hold in his laughter about the concept of democracy. They send Carme.