Life or Death Questions? More on Spider Fuel Tank

[<masochist@domain.elided>]

I pulled the in-tank pump on my Bosch Spider yesterday, trying to identify the
source of a problem that will only allow my car to travel about 130 miles
before running out of gas.

Sure enough, the wire connected to the secondary pump has failed after being
immersed for 18 years.  In the middle of this length of wire was a thin copper
winding around a thicker chunk of carbonaceous material.  Like many
self-taught shade tree mechanics, many electrical components are alien to me. 
So here are my questions...

What is the purpose of that little wound doodad?
How do it work?
And, most importantly, What are the potential consequences of replacing it
with a short piece of wire?

Thanks to Nancy, Ed, Mike, Modelle and everyone else who responded to my
initial query...

Brad
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