Use Arduino to detect low battery state and shut it down
It is not entirely beyond possible, in fact quite possible in theory.

I think the saying 'in theory, theory and reality are the same, but in reality they are not' is appropriate here.

So to monitor voltage, a simple voltage divider circuit can be used, and the Arduino can monitor that, and release a relay controlling the power line. The same relay could be wired to also reconnect when voltage reaches a threshold. I think the circuit actually requires 2 (or more) relays, and technically is it a kind of sensor, but since you indicated a relay was ok, it could work. So given those requirements, do you really need someone to draw it out, or were you just curious?



Simple battery monitoring from http://arduinotronics.blogspot.com/2012/04/voltage-monitor.html