Bankruptcy is the formal dissolution of a corporation that has become insolvent — that is, unable to pay its debts as they fall due. The process exists because dissolution, in the corporate context, is not the end of the matter. There are creditors to be paid (or not), assets to be distributed (or not), and employees to be dismissed (always).
There are two broad forms. In liquidation (Chapter 7 in the United States), the company ceases operations, its assets are sold, and the proceeds are distributed to creditors according to a statutory priority. The company is dissolved. In reorganization (Chapter 11), the company continues operating while negotiating a plan to restructure its debts. The company survives, but in altered form.
Bankruptcy is dissolution with rules. It transforms an unmanageable situation — too many claims, not enough money — into a manageable one by imposing an order on the chaos. Someone decides who gets paid first. Someone decides what the assets are worth. The dissolution is administered.
Not all bankruptcies are failures. Some are strategic. Airlines in the United States have used Chapter 11 repeatedly to shed pension obligations and renegotiate labour contracts. The dissolution is real — jobs are lost, pensions reduced — but the corporation continues. Dissolution, in this sense, is not an ending but a transaction.