There used to be some drill shaft monitors that you could buy that would sound a buzzer when the shaft slowed beyond a certain point or stopped.

I've built one using a single chip solid state timer (type 555) and a variable resistor -- timer coupled to a relay when you wanted to drive something a bit more substantial than a buzzer. As Dennis mentioned, you need a device of some sort that switches on and off with shaft rotation. A timer is a device that charges an internal capacitor and then slowly lets that capacitor discharge. When it reaches a certain level of discharge, one of the pins turns "on". That pin could run your relay. The variable resistor I mentioned is adjusted to make the timer discharge slower or faster and you set that to turn things on or off as the shaft speed hits that level. If the switch turns on and charges the timer before it 'trips' things stay normal. If it takes too long before the switch on the shaft recharges the timer, then it will trip and activate the relay.