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You can certainly make that request, but most employers are only willing to give a severance when it is their desire to obtain a waiver from suit. If you would be voluntarily quitting, they wouldn't have to worry about a suit.
If you are running into issues at work, the employer may be willing to just bide their time and wait for a circumstance that would allow them to terminate legally, without concern for being sued.
That being said, your employer may be willing to extend a small severance in return for you signing a waiver from suit now and leaving without their having to arise a situation that would allow a legal termination. Whether or not they will be amenable to that though is completely up to them.
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