When audio CDs came onto market, promising "perfect sound" forever, lots of folks worried about the demise of good, old-fashioned vinyl LPs. While they did decline to near nothingness for a while, one might notice that not only are there companies once again releasing recordings on vinyl, but even the hardware makers at all levels of the market (from the really cheap all-in-one record players to the ultra high end turntable makers) staged quite a comeback of their own (anyone in the market for a $2K, $5K or even $20K turntable with no arm, no cartridge, no interconnect cable? such stuff is available AND it sells). Online digital, even now cloud-based, delivery of music has certainly forever altered the landscape people my age grew up with where vinyl was everything. Now it's a niche market for hobbyists, aficionados, gear geeks, collectors, retro freaks, etc. BUT, it still exists and has a somewhat loyal following.
So, if film is to vinyl as digicams are to film cams, perhaps there's hope. It would seem to me that the market can support small specialist makers. If Kodak declares bankruptcy, breaks itself apart, etc., it seems to me that some firm will jump in to acquire its film manufacturing assets, licenses, etc. Just as Kobayashi San saw lasting value in Voigtlander as a brand name, perhaps some other enterprising business person will see a way to rescue, preserve or remake Kodak's film business. Of course, their digital and sensor business is completely different story. I imagine that one of their biggest assets is in patents and licenses. I would expect this to be the part that they hang on to in some fashion or sell to someone else who can make something good of it. Don't expect prices to stay low as the market becomes more niche-oriented. Economies of scale will shrink, metal prices will continue to impact film and specialist makers will need higher margins to stay in business.
One last thought: there are still companies that make buggy whips. Not many of them. There are still companies that make pencils. DON'T PANIC. We'll all survive just fine.
My two cents worth...