Dear 100 Hour Board,
What happens if all 15 general authorities die at once? Has the Church made provisions in the event of this catastrophe? How will the next prophet be Chosen? Or would God have to come personally and choose another prophet?
Dear afraid not,
All the keys are only held by those 15 (source), so if they died we'd need someone like Peter to come back and restore those keys. I imagine it'd be like when Brigham Young was proclaimed to be the prophet, in that there would be a large miracle to witness to the Church that that person was to be the next prophet.
Thankfully, it's highly unlikely this would ever happen—if you've noticed, we rarely have all 15 gathered together. During each session of General Conference there's always a few apostles missing. So those would be the ones to carry on the keys if that was ever necessary.
-guppy of doom