This has happened twice. Both times every reward slot was filled. You can’t do anything but keep pressing A and nothing happens. The only way out is to exit the game completely. When you re-enter the game, whichever character you were playing as is dead.
Yep, this actually JUST happened to me and is why I came on here. Happened to me with Orchid during her personal mission where she fights ARIA, every item slot was filled and pressing A didn’t do a thing. Restarted the game and it counted as me failing the mission with Orchid dead.