In the USA, or at least in California, the employer does not pay the unployement benefits to the former employee. The benefits are paid by the state, which in California is http://edd.ca.gov. The employer pays for unemployment insurance. If the employer has relatively few former employees filing for unemployment, that insurance rate may go down over time. The concern over covering the costs of unemployment benefits are related to a possible increase in unemployment insurance premiums.

Source: http://www.calrest.org/tips-for-protecting-your-unemployment...

Yes, in the US most corporations pay unemployment tax (apparently nonprofits and government agencies can get a special reimbursement deal where they pay directly for unemployment costs). As you noted, unemployment taxes increase for corporations with lots of former employees claiming benefits. The fact that it's not direct doesn't eliminate the cost.