It depends. The law does not require you to give severance packages to employees whom you fire. (There is one exception: a handful of states require employers who are closing a facility or laying off a large number of workers to pay a small amount of severance.)
However, if you ever promised the employee a severance package, you should deliver on that promise. And if you ever signed a contract with an employee in which you agreed to provide a severance package, then you must honor that contract. And finally, if you paid severance in the past to other employees in the same position, you may need to continue that policy.
For more about severance packages, see Nolo's article Should You Offer Severance Pay?.