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Even if you had an employment contract, you would still be an "at will" employee unless your contract guaranteed employment for a specified period of time and your employer was releasing you prior to that point in time. Assuming you do not have such a clause in your contract, and it seems unlikely that you do, as an at will employee you can be terminated at any time for any reason not amounting to discrimination on the basis of a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). It doesn't matter whether the basis for termination is fair, reasonable or even true. Thus, you could be let go under the circumstances you describe.
In general, employees have no legal right to severance unless they are part of a "mass layoff" and given less than 60 days notice. A "mass layoff" is defined as the release of 50 or more employees at companies of 100 or more. In this circumstance, something called the WARN Act requires employers to pay however many days wages less than 60 that they provided notice. For example, if the employer only provided 10 days notice, the affected employees would be entitled to 50 days wages.
It is possible for parties to enter into a contractual agreement that severance will be paid in the event of a layoff. However, such agreement must clearly define what triggers severance, the amount of the severance, and payment must be non-discretionary. In other words, if you have an agreement that says "In the event of a layoff, employer SHALL pay employee $5,000" you would have a contractual entitlement to severance because all the terms of the severance are clear. But a mere reference to the possibility of severance does not create a contractual right to severance, as the essential terms for a contract are not there.
So based on what you have described, I must be candid and tell you that no claims for wrongful termination or severance would typically exist. Certainly you can try to negotiate severance, but that would be purely a negotiation. Your employer would have no legal obligation to pay and so you want to be careful not to push to hard.
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