SAIC came under increasing pressure on Monday to save Ssangyong from bankruptcy after union workers authorised a strike, if necessary.
"Our members approved a strike, but we will be very careful on launching an action as many of our suppliers are facing risks of bankruptcy," union spokesman Lee Chang-kun told Reuters.
The union also urged South Korean government to swiftly inject money to Ssangyong not only to save the company but also to prevent potential bankruptcies of suppliers.

A South Korean court also said it has frozen Ssangyong's debts, obligations and assets and will decide in a month whether to accept the company's filing for bankruptcy protection.
SsangYong Motor said late last week it plans to use Korean receivership provisions to avoid bankruptcy while its president and CEO have both resigned.
SsangYong's move may give top shareholder, China's SAIC Motor, a possible exit opportunity amid worries about overcapacity in the global auto industry, analysts in Seoul told the Reuters news agency.