Fraud, misrepresentation, duress, or unconscionability are common defenses you can use if you want to void a severance agreement that you already signed.
Severance packages are compensation awards provided to employees who are involuntarily terminated from their jobs. The packages can include financial benefits, continuation of certain benefits, and sometimes additional services like outplacement assistance.
Revoking Severance: Generally, once a severance agreement is signed by both parties, an employer cannot unilaterally revoke it without a valid legal reason. Severance agreements are contractual obligations, and both parties are bound by the terms.
You can indeed still accept severance even if you're about to accept another offer--in fact, even if you've already accepted another offer (assuming that there's nothing in your severance agreement that prohibits that, which there probably won't be).
More than likely, your former employee will list your actual exit date and not the "severance date" and that is what they would provide. Re-employment can take months so employers would expect gaps in your resume.
Some factors that are often considered include length of employment at the company, your position or rank within the organization, salary, and individual circumstances relating to termination. Some employers adhere to a written contract or employment agreement or policy that was outlined previously.
Most employers offer a severance agreement established by company policy that outlines the financial terms on which the employee will leave the company. Sometimes, employees can negotiate those terms. Regardless, they must sign the agreement to receive their severance package.