Is health insurance for employees through insurance companies—where the company pays the annual subscription and the employee bears a small portion of the cost of some services—halal or haram?

The described scenario could involve either permissible cooperative insurance or prohibited commercial insurance, and the provided details are insufficient to make a ruling. The questioner can refer to the fatwas concerning insurance regulations to distinguish between the two types. If the insurance is obligatory for the company by virtue of an employment contract, then there is no harm for the employee in claiming his right, and the sin, if it is prohibited, falls upon the entity that mandates it, not upon the employee.