I've never heard of employee-paid-for unemployment insurance... only employer-paid-for unemployment insurance. Are you paying into an employee funded unemployment insurance plan?
What is the difference whether or not the employee writes the check to insurance company or the employer does? Either way the cash is coming from the same pot. Remember, the employer hires the employee to help the employer make money. Some of that money is paid directly to the employee as salary. Some is paid to insurance companies as a benefit for the employee.