Filing for bankruptcy does not mean going out of business. It means that they hopefully get some help in paying off their debts, maybe some debts will never get paid at all. But they will continue to fly, although it is possible that some flights could get cancelled. Companies use bankruptcy to try to make it so they can stay in business, not end business. Unfortunately, the people who may be most affected are their employees who may lose some benefits, possibly lose some of their pensions, may in fact lose their jobs. But they will continue to fly planes.