Basically, a severance agreement is a waiver or release of liability that the outgoing employee signs, protecting the business from lawsuits. These agreements are usually part of a larger severance package that includes compensation, outplacement services, and other benefits in exchange for the employee's signature.
Generally speaking, employees who are fired are not offered a severance package—particularly when they are fired for misconduct. However, some fired employees are offered a severance package in the hope that they will “go away” after receiving the package.
You probably won't be able to get Unemployment if you quit for personal reasons or because you did not like your job. You might not be able to get Unemployment if your boss says you were fired for “misconduct.” Misconduct can be things like poor attendance and being late.