Let's be clear. You can't ask an employee to release or waive their right to unemployment in my home state of Florida. Period.
Here's what the statute says if you don't believe me:
443.041 Waiver of rights; fees; privileged communications.—After a brief bout of research, it looks like lots of other states also prohibit this practice. I've found laws prohibiting such waivers in New York, Texas, Minnesota, Maryland, California, North Carolina, and Missouri. That's a pretty good sampling of pro-employer and pro-employee states, so I'm guessing your state may prohibit this as well.
(1) WAIVER OF RIGHTS VOID.—Any agreement by an individual to waive, release, or commute her or his rights to benefits or any other rights under this chapter is void. Any agreement by an individual in the employ of any person or concern to pay all or any portion of any employer’s contributions, reimbursements, interest, penalties, fines, or fees required under this chapter from the employer, is void. An employer may not directly or indirectly make or require or accept any deduction from wages to finance the employer’s contributions, reimbursements, interest, penalties, fines, or fees required from her or him, or require or accept any waiver of any right under this chapter by any individual in her or his employ. An employer, or an officer or agent of an employer, who violates this subsection commits a misdemeanor of the second degree, punishable as provided in s. 775.082 or s. 775.083.
For some reason I have to say this about every ten years or so. The management-side employment lawyers know better. It's the employers who handle business/corporate law who decide to dabble in employment law who need to be reminded.
Therefore, I am saying it. Now cut it out and stop torturing people who have lost their jobs.