It depends on the load and battery ability to supply necessary power.
In my case I have a Super Capacitor (or Ultracap) as the “battery” and it can handle a maximum current of 630mA (130mA continuous), so I detect the (5V from Solar) power “fail” and switch to “battery mode” - shutting down certain functions.
If the “battery voltage” goes too low, I isolate it and put the ESP32 into (timed) Deep Sleep.