When a person or company is no longer able to pay the amount of debt they owe, they can file bankruptcy and be given options for relief.
There are different types of bankruptcy filings available (found here — chapters 7-15) in different situations to people and businesses. Before filing, the debt would have to have accumulated to a point where there is no mathematically feasible way to repay it all. There may be a way to repay some of it, however.
It may mean that a business is able to continue to keep its doors open, with payment plans to service some of the outstanding debt, but this is likely after some assets have been liquidated to settle some of the creditors' claims.
Obviously, this process is going to affect the creditworthiness of the entity filing, but the idea is that the filing party is able to move forward with a fresh start and a manageable amount of debt.