If you cross proces slide film to C41, most often the base isnt clear. The color of the base changes from basic brown-yellow to purple or cyan or whatever, depending on the film (and maybe the state of the chemicals used). Some films are close to clear, most are not.
You can process any still film with B&W chemicals, because they all use silver-stuff as light-sensitive layer.
C41 dev. will develop a B&W neg and a color neg under this. Bleach+fix will remove all the silver from the film, because bleach will return all the silver to its original state (that it is in before exposure), so fix will remove all of it.
E6 instead, will first develop just a B&W neg on the film. This will kind of "block" these silver grains from getting developed in the next step, which is colour developer. This developer will also chemically expose rest of the halides or grains, so that you will get a positive colour image. All of the silver is exposed, so without bleach your image will be completely black. Bleach and fix will again remove all of the silver, and you are left with a color positive, as there is no color negative under the BW-developed grains.
Just like you can cross process any E6 and C41 color film, you can also develop B&W positives from regular BW films. You dont need Agfa Scala or such, but you do need some special chemicals. This process is explained for example on the Ilford website
(however, the amount of the "fixer" added to the developer seems too big there - at least according to my friends experience. So if you are going to try it, begin with much less or none at all. More info from the PDF on Ilford website and of course, other places in the internet)
Still I am wondering, how Kodachromes can be cross-processed as it really is a completely different process. You can develop BW negs from them but cross-processing them in another process, I dont know what will you get really.