Maybe timing chains chatter when they stretch? Could be a lot of possibilities to be honest, you should check them all one by one. Never experienced this in my corolla though nor did my friend's from DSRLeasing wife.
My 2009 Corolla just started rattling upon start up. I isolated the rattle to be coming from underneath the car. When I viewed underneath the vehicle, I observed a heat shield laying on the exhaust pipe (I think - I had no jack to get under for a better view). I dont think it is on the drive shaft but it is in the middle of the under belly. Have not checked out how to fix yet. I will post this later.