We will use a Texas Instruments BQ24072 in our power board to monitor the battery.
-PoE or solar will charge -Most of the time, circuit will work on battery.
When disconnection the Vin, one would assume the battery takes over.
datasheet p3 Vin voltage range between 4.35V and 26 V datasheet p4 UVLO Undervoltage lock-out VIN: typical 3.3 V
This would suggest that everything stops working when Vin is too low.
Answer: ok, datasheet p16, everything shuts down but battery is "connected" to out
UNDERVOLTAGE LOCKOUT (UVLO)
The bq2407X family remains in power down mode when the input voltage at the IN pin is below the undervoltage threshold (UVLO). During the power down mode the host commands at the control inputs (CE, EN1 and EN2) are ignored. The Q1 FET connected between IN and OUT pins is off, and the status outputs CHG and PGOOD are high impedance. The Q2 FET that connects BAT to OUT is ON. (If SYSOFF is high, Q2 is off). During power down mode, the VOUT(SC2) circuitry is active and monitors for overload conditions on OUT.