At-will employment is a doctrine in which an employee can be dismissed by an employer for any reason without having to establish "just cause" for termination, and without warning. The basis for this rule is that an employee may be similarly entitled to leave his or her job without reason or warning. In workplaces with a trade union and a collective bargaining agreement, and in many public sector jobs, the normal standard for dismissal is that the employer must have a "just cause". Otherwise, subject to statutory rights, such as protections against discrimination and/retaliation, the general principle is that an employee may be discharged without cause and without notice.
Unless your employer has a policy to give severance or you are covered by an agreement that provides severance, your former employer has no obligation to provide severance.
With that said, there may be circumstances in which you might be able to negotiate a severance package. The facts that you provided are not sufficient to determine whether you are in position, or have leverage, to negotiate a severance package.
You might benefit from consulting with an experienced employment law attorney and having them evaluate your circumstances. The California Employment Lawyers Association maintains a list of employment law attorneys who represent employees against employers. Follow the link to: www.cela.org.
Unfortunately, the law only mandates severance in certain limited circumstances involving mass layoffs at large companies. Otherwise, absent a contract that expressly entitles you to severance upon separation of employment, your employer has no legal obligation to pay you anything beyond what you actually earned.
This answer is a general interpretation of the law and is not fact specific to your case. Likewise it does not create an attorney-client relationship. You should seek an attorney for a review of your specific facts and documents.
Severance packages are not required at termination and are at the discretion of the employer. Moreover, employers in California are not required to provide a reason for termination unless there is a contract to the contrary.
Sadly, no you aren't entitled to a severance package. Some employers offer severance in exchange for waivers of any rights to challenge the termination, but they are not required to do so. Otherwise you were most likely an "at will" employee. This means you could be terminated for any reason, or no reason at all, at any time so long as it isn't based on discriminatory reasons (i.e. because of race, sex, national origin or another protected classification), or your having engaged in a protected activity, or in violation of the terms of a contract or collective bargaining agreement. Being “at will” also means that the employer was not required to provide advance notice of a termination decision and was not required to justify the decision with “good cause.” Sorry...
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You may be able to negotiate a severance package IF your employer has a pattern or history of paying severance pay to similarly positioned employees or if you have any potential legal claims such as overtime, earned, unused and unpaid vacation or PTO, discrimination based on a protected class, etc. Otherwise, the employer is not legally obligated to pay severance unless you had a written contract providing for it. If you believe you have any legal claims against your former employer, call an employment law attorney to discuss. Also, if you did not receive your final check including any earned and unused vacation or PTO, you are owed one day's pay for each day you have/had to wait to receive it plus your attorneys' fees will be paid by your former employer. An employer does not have to provide any reason for termination.