Unless you have an employment contract which contains a provision requiring two week notice, either party to the employment relationship may terminate that relationship at any time. This means that if you give notice and the employer decides to end the relationship immediately, it is under no legal obligation to pay you for the remainder of the two weeks. It is tempting to provide the professional courtesy of a two week notice but many employers do not respond well and end it right away. Be aware that there are risks if you give notice.
They say you get what you pay for, and this response is free, so take it for what it is worth. This is my opinion based on very limited information. My opinion should not be taken as legal advice. For true advice, we would require a confidential consultation where I would ask you questions and get your complete story. This is a public forum, so remember, nothing here is confidential. Nor am I your attorney. I do not know who you are and you have not hired me to provide any legal service. To do so would require us to meet and sign written retainer agreement. My responses are intended for general information only.
No. Not if you are an at-will employee (no written contract for specified time), but you are entitled to your wages for work performed plus any earned and unused vacation or PTO on your last day of employment if you give at least 72 hours' notice or your employer terminates your employment.
As Mr. Kirschbaum and Ms. Karlia stated, your employer is free to fire you at the time you give your notice – or at any other time – unless you have a contract that states otherwise, the employer's policies require the two weeks notice, a union-employer contract requires the notice, or the employer is treating you differently because of your membership in a protected class (race, sex, disability, age over 40, etc.
This can put an employee in a real bind, as you note, because of course you don't want to be without an income.
Please see my guide to at-will employment in California which should help you understand employment rights: http://www.avvo.com/legal-guides/ugc/a-short-summary-of-california-at-will-employment.
If your job requires substantial training or is at a fairly high level, if it is hard for the employer to find employees to fill the position, if you are the only one or one of a few who can do the job, it is less likely the employer will terminate you on the spot because it needs someone to do the work and perhaps train the next person. However, if your job can be filled by many people or your duties can be temporarily distributed to other employees, the employer may feel free to let you go right away. In either case, there are no guarantees. You might discreetly ask some of the long-term employees what the employer has done in the recent past to try to get a handle on it.
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I agree with everything my colleagues have to say on the subject. Perhaps the only thing I can add to the conversation is a bit of perspective.
While it is certainly courteous and professional for an employee to provide notice of leaving the company, it does put the employer in an awkward situation.
Specifically, the employer will ask itself questions like these. Will the employee misappropriate company information? Might the employee do something to sabotage the company? Has the employee already "checked out" mentally such that the company is not likely to get much effort for the next couple of weeks? Will the lackluster performance rub off on coworkers? Could it be demoralizing to the rest of the staff to hear about how the employee is moving on to better things?
Once it is clear that the employee's loyalties and/or focus have shifted, the employer may feel it does more harm than good to wait out the two weeks.