The company and union leaders are scheduled to argue in a bankruptcy court whether or not the firm can toss out its union contracts.
The hearing is expected to last through Wednesday, CNNMoney reported.
Even unions have agreed the company would likely be liquidated if union members strike, which they have pledged to do if the court allows the company to walk way from its contract obligations.
"We would no longer have cash to keep operating. All Hostess Brands operations would shut down and liquidation would begin," the company said in a letter sent to employees Monday.
"The 18,500 jobs, plus the health insurance that comes with it would be lost for good," the company said.
Hostess Brands is making its second appearance in bankruptcy court since 2004.
The company, formerly known as Interstate Bakeries, emerged from bankruptcy with a new name in 2009.
The company is well known for its lineup of sweet novelty items, such as Twinkies, Hostess Cupcakes and Drakes Cakes, which have been on the market since 1888. It is also the maker of Wonder Bread, which has been on grocery store shelves for 90 years.
About three-quarters of its workers are represented by the International Brotherhood of Teamsters and the Bakery, Confectionery, Tobacco Workers.
But neither management nor unions sound ready to negotiate a compromise beyond what is already on the table.
"We put an offer on table with $150 million in concessions. There is not a chance our members would accept (the firm's offer). They won't work for nothing," Teamsters Secretary-Treasurer Ken Hall said.