HI,
in case you use a microcontroller:
It´s almost standard in my microcontroller designs to "watch" the power supply.
In simples case I just have a power supply monitor (for 3.3V for example) that asserts a RESET when power is too low. This RESET may be used to stop the microcontroller , but also the disable other parts of the electronics,( like a MOSFET driver for example).
But it could also watch about mains to get an "early alert" to smoothly power down everything, save states / variables in an EEPROM... and so on.
It depends on "what could happen ... if". If you fear to casue a n erroneous short circuit on the battery ... and risk overheat, explosion, fire ... then you definitely should add some protection.
Klaus