The Government has said the crisis at Harland and Wolff shipyard is 'a commercial issue' amid calls for the business to be re-nationalised.
Workers stayed out overnight at the famous east Belfast site and have said they will remain there until a solution is found.
However, it is looking increasingly unlikely that the government will not intervene with administrators expected to step in on Monday.
They are calling for new Prime Minister Boris Johnson to bring the shipyard under government ownership to save the 130 jobs currently operating there.
Once employing around 35,000 people in its heyday, the yard now specialises in marine and wind engineering with a significantly reduced number of staff.
Harland and Wolff's parent Norwegian company has been under financial pressure with uncertainty shrouded around the Belfast site.
More than 100 people attended a rally held by trade unions outside the gates of the yard on Tuesday afternoon.
Harland and Wolff staff member Paul Beattie spoke of his frustration at the possible closure.
"The workforce here are highly skilled and committed, it’s not good enough for anyone to shrug their shoulders and say we should walk out of here on Wednesday and never return.
"We are disgusted at the idea of companies sitting out there like vultures waiting for this place to go into insolvency so they can swoop in."
Boris Johnson is expected to arrive in Northern Ireland over the coming days with workers wanting to meet the new Conservative leader to discuss their concerns.
A spokesperson for the government said: "The Government has every sympathy for the Harland and Wolff workers at a time of great personal uncertainty.
"We will work with partners in Northern Ireland and Westminster to understand the situation and do all we can to support, but it is ultimately a commercial issue."
The Government added that Secretary of State Julian Smith has spoken with Invest NI and ministers as a matter of urgency.