According to my husband’s previous paycheck stubs (out of work for a year and a half now, except for the whopping 70 hours he worked in July! He is/was a union tile setter.) unemployment insurance tax is deducted. The employee pays in and so does the employer. There is a limit on how much is deducted for the employee per year (NJ), no idea how much the employer has to pay in.
In most states UI taxes are borne by the employer only.