In Hungary, as in other EU countries, Directive no. 883/2004/EC and Regulation no. 987/2009 on the execution of the directive is in effect, which regulates the social security status of migrant employees.
As a general rule, employees are insured in the state where they work. An exception to this rule is short-term assignment (STA),when the employee may remain insured in the country of origin for a period of maximum two years according to the main rule.
Managing director
If the company’s managing director is not secured in any EU member state then the company must pay social security contributions in every month after the director even if he/she is not an employee and not get any wages. I would cost cc. 250 EUR per month. In exchange for that the director could use the social security system in the EU.
If the director is secured somewhere in the EU you should provide us the director’s “A1” certificate ASAP proving the director employed/insured in an other EU member state, and your healthcare contributions-social taxes are already payed there. This certificate is issued by the competent authority of the country where the director is insured.
Please note that even if you have a private health insurance you have to be insured under the national social security system too!