They've filed for Chapter 11 Bankruptcy. Chapter 11 is not the same as Chapter 7. They'll still operate. It's not like they're going away. At least, they don't have to. If they manage the company right after they come out of the bankruptcy, then they can continue on.
This might be a good thing for Kodak. In their present form, they've just been wheezing along, barely being kept afloat with life support. Maybe after the restructuring they'll get rid of the dead weight, the divisions that have been holding them back, and they'll be turned into a lean, profitable company.
Chapter 11 doesn't have to be the end.