Tore down a completely puffed, dead, 0V cell. It was still air tight.
So basically, it's a stack of copper anodes (-) & aluminum cathodes (+) separated by plastic. They're soaked in a fluid. The plastic conducts lithium protons between the terminals, but not electrons. The plastic is why they're called polymer batteries.
The copper sheets (-) are coated in lithium + graphite. The aluminum sheets (+) are coated in lithium + cobalt. The positive lithium protons transfer through the polymer from the - to the + electrodes. The negative electrons transfer through the load from the - to the + electrodes.
Neither the anodes or cathodes reacted violently, even in water. Despite not being air tight, the electrodes stayed completely black when wrapped up. Then some of the anode turned white when completely unwrapped. Since it was completely discharged, it would have been residual lithium. It would have been more exciting if it was fully charged. The cathode side didn't change color.
They're all connected in a parallel fan at the electrode.