Bob Shanebrook points out in his book that all or virtually all of Kodak's film base support is made in-house. Film supports are made for other applications than photography though so the production of support such as Estar or Acetate is not dependent on Kodak's consumption of the material. They are a minor player due to their own capacity.
The major differences in films industry wide is the subbing or lack thereof for each application. Kodak makes unsubbed and subbed film supports. You can buy subbed or unsubbed supports from ICI in England for a variety of applications and IIRC, Ilford buys from ICI. Jim Browning used ICI produced Melenex support for his dye transfer Matrix Film. It was pre-subbed to a given standard for the dye transfer process.
There will be no major problem if Kodak stops making (or buying) support. In fact, they may stop making entirely and start buying which will probably be good in a sense. Prices will go up though due to increasing labor and materials costs, but not because Kodak changes anything.