From your description, the dead-battery case is CCG2 is power off and power on with VBUS of Type-C. If you are going to support dead-battery on CCG2, you need make sure your hardware design have supported deab-battery case:
1. VBUS_C_CTRL is LOW by default, so that the VBUS can power on CCG2 board.
2. Make sure power consumer path is enabled with VBUS_C_CTRL drive to LOW.
3. Make sure the dead-battery supported have been enabled in configure table.
CY4521 hardware schematic can support dead-battery, you can refer to it.
In our schematics VBUS_C_CTL is low when there is no power to the CCG2 board. In the application the default status of VBUS_C_CTL was high and we modified the default status to low. Now the Dead battery condition is working fine.