Allowing companies (even ones that are large and considered important like airlines) to "fail" just means that they'd have to go through bankruptcy proceedings and that the owners would lose some money - it doesn't mean that their operations will shutter, or that the planes will suddenly disappear, or that everyone in those companies will suddenly be out of work.
There are many examples of how this works - a recent one being PG&E in California, who filed for bankruptcy last year. Our electricity is still running and the linemen are still working.