Unemployment benefits are not contributed to by the employee. The employer is the one who pays into that fund. It is up to the Unemployment Benefits agency in your state to determine if you should or should not be receiving benefits and they are the ones with the power to demand that you pay back the funds given. The employer may appeal the rulings of the Unemployment Benefits agency, but unless there is some other serious issue cannot privately sue a former employee. If your employer is the one suing you, you should get an attorney right away to see exactly why they have brought this suit. Obviously your employer has an attorney, so you need one also.
I agree with Ms. Summers...something isn't right here or you are seriously confused. Your employer should not be filing a lawsuit against you for seeking unemployment benefits, and if it did then you should immediately hire an attorney to represent your interests.