They can't simply "wind down" the business because that would violate their fiduciary duty to the shareholders. You can't just tell your investors "I give up!" and go home. Besides, the moment they announced "we're winding down the business," the stock would immediately go to zero or close to it and the bankruptcy would be immediate.
Of course they can "wind down" the business. This is exactly what their fiduciary duty to their shareholders is if they know that the business is not viable (i.e. they are supposed to minimize the losses to the shareholders). Businesses do this all the time when continuing the business just destroys shareholder value. This is what Kodak should have done long ago.
Kodak's management who are far smarter than 99.9% of the posters on
Never attribute to stupidity that which can be explained by greed.
Lend money to a bad debtor and he will hate you.