But tough toodles for them. I would have took that severance agreement straight to a lawyer.
Returning to the topic of the thread, the practice of forcing employees to train replacements on pain of not getting a severance is pretty common. If you refuse and the company terminates you, you qualify for unemployment. If agree to the servitude and severance, you've just executed a voluntary quit and the employer has no obligation with respect to unemployment compensation. If you don't do as agreed, the severance payments stop and you have no recourse.
If you have time on the books, go on vacation. You'll collect more money and retain benefits vs taking a lump sum with a higher withholding rate and an immediate termination of benefits. Use the "vacation" time to find another job. Assuming you land one, issue your two week notice and go away.