The BQ2562x family of charger ICs can be configured to operate in a variety of ways via I2C communication. They can also operate in 'default mode' without host control.
The BQ2562x family of devices does not have non-volatile memory. When both input adapter at VBUS is removed and battery is dead register settings will return to their default values defined in the register map section of the datasheet.
As long as either VBUS input is above typ 3.15V or battery voltage is above typ 2.2V (or 1.8V depending on VBAT_UVLO register setting), and the watchdog timer is disabled (REG0x16 bits 1:0 = 00) or reset before it expires register configuration will remain as initially set.