When this happened the second time in canon she threw everything into healing said wound, even though it massively overextended her powers until they snapped back and fatally injured her instead
there's no way she won't have some kind of fit over this. most likely Saya would cry, go ballistic and/or start murdering. depends on context! she might also consider feeding her blood to her mouth to mouth to prevent her from dying but have a moral conundrum about turning someone else into a chiropteran, but also letting her die!
Aside from the immediate "I'm going to put the thing that did this down" reaction, there will be some denial, likely some screaming to get back up, and hoping someone close by is trained in healing or medicine, because Amelia would not let Kainé go without a goddamn fight.
My character takes a fatal blow for yours. What happens next?