Quinn Insurance representatives have warned that even if the company recovers from its problems, it could still suffer significant job losses.
The company, which employs 600 people in Fermanagh, went into administration last week and was prevented from doing new business in the UK.
A delegation from the company met with the Assembly's Enterprise Committee at Stormont on Thursday.
They had hoped to establish whether the Executive could provide assistance.
The Republic's financial watchdog has partially lifted the trading restrictions, a move which allows the firm to write new insurance cover for provisional licence holders in the UK, about 10% of their business.
After the meeting the Enterprise Committee, the company's David O'Donnell said: "The business is resourced for 100% optimum operation capacity.
"If we get back up tomorrow, that operational capacity has been reduced, and it is an inevitability that there will be job losses."
Meanwhile, the Assembly Finance Committee, following a recommendation from the Consumer Council, is to call for an inquiry into the high cost of insurance in Northern Ireland.
Sinn Fein MLA Mitchel McLaughlin accused the industry of "playing fast and loose" with NI consumers and said there was a lack of competition.
The Consumer Council said that NI households pay an average of £278 more for all their insurance than in the rest of the UK.
Mr McLaughlin said all insurance companies were dealing with a small number of clearing houses in Northern Ireland.
Joleen Cunningham from the Consumer Council told the finance committee that the establishment of the new Department of Justice could have an impact on lowering the cost of insurance in Northern Ireland.
"The devolution of policing and justice has created the opportunity for the Northern Ireland Assembly to address some of the issues around higher insurance and around the costs issue of compensation levels," she said.
"Compensation levels are reviewed every six years by a committee of judges, barristers and solicitors. They are not actually set in stone."
She added: "We think an assembly-led committee, or cross-working within departments, could look at whether the benefits of higher compensation levels here outweigh the detriment to consumers with the higher levels of insurance."
The Consumer Council said overall NI households are £160 million worse off than the rest of the UK.
Car insurance costs 80% more in Northern Ireland - an average of £282 extra than in Britain, it said.