Can a quantum particle anihilate itself by interference?

I was thinking of the often cited experiment where electrons are fired one by one at a double slit, which results in an interference pattern on a screen. The bright lines are obviously where an electrons hit, but what is happening in the dark bands. I believe the "clical" explanation is that in the dark bands a peak of one wave coincides with the trough of another wave and cancel each other out. Am I wrong in thinking that every electron fired at the double slit results in a bright spot or can an electron effectively destructively interfere with itself and destroy itself.