arya theory that's about 75% a friend's and 25% mine: waif returns to jaqen saying it's done. jaqen says "a girl still lives" and sends waif back out to finish the job. in the meantime, arya realizes she's gonna die by bleeding out. she returns to the hobaw and tells jaqen to give her the death juice and promise her that he will kill cersei (and maybe the mountain and ilin payne). maybe she says to take her face and use that to show cersei whose responsible for her death in the last minutes. jaqen then gives her the death juice which is transformed into the cure juice. the many faced god sees her sacrifice, her gifts, her whatever, and spares her, he has more use for her. then jaqen tells her a death is owed and she must go find and kill waif.

this fits a bigger theory i have that jaqen's plan for arya has this entire time been for her to kill cersei. he doesn't want her to be fullblown fm. there are inklings in the dialogue that the fm is a sort of moral institution that kills based on judgment instead of just money (like providing mercy for slaves by the first fm in valyria killing masters). fm hasn't been contracted to kill cersei, but they want cersei dead nonetheless and they know arya is the way to do it. this has all been training to get to that goal imo.