Windshield washer pumps move the windshield washer liquid from the reservoir to the windshields. It is why the pumps may get damaged if you try to use them when the liquid tank is empty. But the liquid may get emptied in case of a broken pump too. 

The signs of a broken windshield washer pump are:

• An uneven spray of the liquid
• Unresponsive pump
• Quickly emptying windshield washer fluid reservoir

A lot of automotive experts suggest checking the windshield washer fluid tank once a week. It helps you in the early detection of the empty reservoir or possibly broken pumps, jams in the nozzle, etc.