Not contesting unemployment: legal or illegal?

Q. We have a challenging employee who is not really a poor performer, but is generally disliked by her co-workers. She is a gossip and games the system on our attendance policy. She seems to needlessly start minor squabbles with other employees. Recently, this employee approached HR and offered to resign if the company would agree not to fight her request for unemployment. We feel like this is a good opportunity to get rid of a problem employee without terminating her, and unemployment benefits would be a small price to pay. Is there any reason why we shouldn’t accept her resignation and agree to not challenge her unemployment claim?