If you drive a hybrid car, you might not be aware that it actually has two batteries: a low-voltage auxiliary battery and the much larger traction battery. What happens when a hybrid battery dies depends on which of those batteries you're having trouble with. The 12-volt battery wakes up the car's computers and runs conventional accessories. The traction battery stores energy for the electric motor and, through a DC-to-DC converter, helps keep the 12-volt system charged. If that small battery is dead, the car may be completely inoperable even when the high-voltage pack is fine.
The larger pack should never run completely empty during ordinary driving. In a conventional hybrid, the gasoline engine and regenerative braking recharge it as the car moves. A plug-in hybrid that shows zero electric miles has usually reached the end of its EV-only range, not suffered a battery failure; the vehicle then switches to hybrid operation.
If the traction pack deteriorates or develops a fault, the car may keep moving with reduced power, or it may stop and refuse to restart. The outcome depends on the model and the fault. And even though hybrids have a gasoline-powered engine, it's not a spare drivetrain waiting to take over. On many hybrids, the electrical side also starts the engine or provides some of the propulsion needed to move the car. A high-voltage battery warning needs prompt attention.