I guess this is why mobile phones dont usually allow running without a battery
But my guess on what would happen (basic logic, I dont know if the chip is going to interfere in some way) if you attach a battery in different (extreme) states while the AC adapter is in CV mode (4.0V):
* Full battery (4.2V): I think it would essentially switch to battery power until the battery voltage hits 4.0V, then slowly transition to AC power (keeping the battery at 4.0V)
* Really Empty Battery: It would dump all the current the it can provide to the battery to bring its terminals to 4.0V. The AC adapters are rated at 2A, with software one cannot program a charge current over 1.7A (but dunno). There may be other limits.
Those would be the "think what a 4.0V regulator would do when a battery is inserted onto its output terminals"-type assumptions.
I went out to read what the TPS65950 should do (according to its TRM) when it senses a battery in CV mode. It should transition to Off Mode. I'm not sure whether that means that the pandora should transition to running on the battery, or totally turn off.
It might be that this is happening. People turn on the pandora with only AC power (CVM), then they attach the battery. The TPS65950 turns off the charge circuit, and the software is unable to control anything, thinks that it is on AC even though its actually on battery or something. The battery gets drained below safe limits and the pandora turns off.