Most Watched Tv Shows: [EVERYTHING] Arya Stark and The House of Black and White

Hi, I'm super new to this subreddit and GoT too tbh so I'm not sure if this has been asked before.

How did Arya see her own face on "Jaqen's" dead body after he drank poison in the House of Black and White? I thought that the Faceless Men can only use the faces of those whose deaths they are responsible for. Arya isn't dead, so how was her face one of the faces on the body of no one?

Thanks for any insight!