1996 Jeep Cherokee Car dies while driving

The car won't start, sometimes, when it do it will die will I'm driving. I have to let it sit for a while, then try it, it seem to be getting worse, about starting. A local car parts store told me it was the "starter relay" that caused it not to start. But my question is will the starter relay cause it to die while I'm driving, shutting off all power to everything? No lights, no horn, no nothing.