Is it permissible for employees to voluntarily subscribe to the health insurance offered by their company, given that the company does not deduct any fees from them?

If participation in insurance is optional, it is not permissible unless it is a legitimate cooperative Takaful (Islamic insurance). However, if the employer has subscribed to an insurance system for its workers and paid the subscription fee, then if the insurance is cooperative, there is absolutely no harm for the employee in benefiting from it. But if it is a prohibited commercial insurance, the employee may only benefit from the amount that was subscribed for him.