Well, unless you have a contract that spells out a term of employment and duties, etc., all employment is employment at will. You can be terminated at any time for good cause, bad cause or no cause (excluding prohibited discrimination).
In this case, in lieu of severance pay (which they are not legally required to give) they agreed to give you one month notice of termiantion (something else they are not required to give). During that time they are asking you to finish up some work and to train an employee who will try to absorb your workload. This is permissible.
While such a situation is distasteful (believe me, I understand), I would recommend acquiesing to their demand. The severance pay agreement might not be enforceable for want of consideration
(I'd need more information to determine that) but in any case, it would likely cost more in a legal squabble over it that you would stand to get.
I'm sorry. I know thats a crappy answer, but thats what I think is the best way to go.
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