[Ron Ramirez]

Jerry is correct on both counts - in that your 42-355 never had a back, and that the "mystery" wire is part of the FM dipole.

I would not remove the white or black wires, but leave them in place. Notice how the two wires terminate in a plug which plugs into the back of the chassis?

There are ways to make that old 42-50 mc FM band useful:

http://www.somerset.net/arm/fm_only.html

I should add that I have never tried any of those converters, but I'll have to do so sometime.