There is a type of pressure switch that will cut the pump off if the pressure falls below a pre-set level. The pump cuts on at about 35psi and off at about 65psi and the pressure tank holds pressure on the output lines. If the pressure drops below a pre-set level (20psi usually) it will cut the pump off completely. The pressure should only drop that low if the well goes dry. Otherwise the pump and pressure tank keeps the pressure high enough to keep the switch from tripping. It's a safety mechanism to prevent burning up the pump motor if it runs out of water. Where I live in Chattanooga Tennessee area you can get one of those pressure switches for under $30.

Here's one on Ebay:
WATER WELL PRESSURE SWITCH WITH PUMP PROTECTION

Pooh Bear