I originally thought that it might have been considered as a "Green" (as in "Spinach and Other Greens") and pressure canned that way, but asked specifically about that late last year and was told no (most unequivocally). The NCHFP told me that cabbage was much more rigid and dense than spinach so using that process would result in it being underprocessed which could be a botulism risk since it is a low-acid food. They later incorporated my question into the January 2014 blog post (see Replies) http://preservingfoodathome.com/2014/01/28/got-the-wintertime-greens/#comments
Please note that if you look up the process on the NCHFP website (http://nchfp.uga.edu/ - I highly recommend taking their online course) it does not specify what "other greens" are included. But the most recent (2013) Ball Blue Book (which every home canner should have) does and cabbage is NOT included in the list.
I forgot to ask about soup, but I figured that if it was fully cooked, a small amount could be used in a soup and canned using the "half solids" rule. Wrong again! A recent post on the NCHFP blog addressed the use of cabbage (and cured or brined meats such as ham or corned beef, in case you have some of that left over as well) in pressure-canned soups - don't do it! As far as I know, there are no laboratory-tested recipes for any soup containing cabbage (NCHFP doesn't have one and Ball told me that they do not have one). NCHFP recommends adding greens and these meats when reheating the soup. http://preservingfoodathome.com/2015/03/05/simply-soup/
Now, if you'd like a cabbage and corned beef soup to make fresh this weekend, here's one I plan on trying with the 2 pounds of cabbage pictured here