Harland and Wolff has entered administration, with accountancy firm BDO formally appointed to oversee the Belfast shipyard.
Having employed more than 30,000 at its peak, the move could now put 120 jobs at risk and spell the end of the iconic firm, best known for building the Titanic.
Unions representing workers have called for the shipyard to be renationalised.
They argue it would be cheaper for the government to keep the shipyard open.
However, the government has said the crisis is "ultimately a commercial issue".
The Northern Ireland Office said NI Secretary Julian Smith "understands the impact" uncertainty over the shipyard will have for workers and their families.
It said Mr Smith "had made it clear that he will continue to do everything he can to secure the future of this historic site and ensure workers' interests are protected".
A spokesperson for BDO said: "The team at BDO have engaged immediately with Harland and Wolff employees and other stakeholders to take all necessary steps to ensure they are supported throughout the administration process."
A week ago, workers took control of the site and established a rota to ensure their protest continued around the clock.
On Monday, union sources said staff were given redundancy notices saying the business would cease trading in the evening.
The workers, though, said they would continue their protest.
"These workers are saying 'we're staying in until we win'. This occupation will continue," said Susan Fitzgerald of trade union Unite.
"There's huge interest in this yard, but the real interest needs to be coming from Boris Johnson."
Speaking to BBC's Good Morning Ulster, Michael Mulholland from GMB Union outlined a plan for the yard's survival.
It involves administrators giving the workers and unions a period of time to find a buyer for the shipyard that will protect jobs.
Asked if the proposal had a precedent, Mr Mulholland said: "I'm not aware of any precedent but we are in dire times.
"If it needs a creative outlook, the trade unions are prepared to do that and we only hope that government and administrators will come along on that journey with us."
After the administration announcement, Democratic Unionist Party (DUP) leader Arlene Foster said she and the party's East Belfast MP Gavin Robinson had met GMB and Unite.
She said they had a "shared vision" for the yard.
Shadow Chancellor John McDonnell said Labour would have nationalised the shipyard and he accused the government of betraying the workers.
Mr McDonnell, who visited Harland and Wolff staff in Belfast on Monday, said the shipyard has the potential for future work.
Harland and Wolff's best known vessel is the Titanic, which was built at the yard between 1909 and 1911.
The firm had been up for sale amid serious financial problems at its Norwegian owner.