In short, no. According to the FLSA, employers are only required to pay terminated employees’ wages through their last day of work, as well as for any time the employee had built up (i.e. unused vacation days).
That being said, many companies do offer severance pay and/or packages. It’s important to note that severance pay and packages are included in an employee’s contract and decided upon along with the base pay and any other forms of compensation. Generally speaking, severance pay could range from a week or two worth of pay for each year the employee has worked up to an entire month’s pay for each year worked.
While there is no law requiring employers to pay severance, employers are required to offer COBRA (Consolidated Omnibus Budget Reconciliation Act), which gives recently terminated employees the right to prolong their health benefits provided by the company. Note that in this scenario, employers can require employees to pay the premium for their health coverage.