Thank you for the information and your question. You are right to question what your employer has told you since it is both misleading and incorrect. It is misleading in the fact that they imply that if they do not object to your unemployment
claim that you will thereby qualify for unemployment. The fact is that although the employer can dispute
or not dispute a claim, it is the State that decides if someone is eligible for benefits based on the facts. The statement that is incorrect, is their statement the a voluntary quit in lieu of termination
will make you eligible for UI benefits. That is not the case.
The State, on the other hand, gave you better information, although no one, other than the person who reviews the facts for the UI commission after they have gathered them all, or an appeal hearing officer, can tell you with certainty whether or not you will qualify for benefits. However, to qualify for UI benefits, a claimant must either have been terminated without "cause" or misconduct, or
they must have quit for "good cause" attributable to the employer. In the first case, if the claimant is denied UI benefits, it would be the employer that would carry the burden of proof to show that the employee intentionally, or through gross negligence, failed to perform their job properly.
In the case of a quit for "good cause" attributable to the employer, it is the employee who carries the burden of proof to show that they quit because the employer did something unlawful or so severe that a reasonable employee in their same position would have quit. I can tell you that resigning in lieu of termination, unless the termination is illegal, is not good cause to quit.
The types of things that are good cause are if the employer is violating the law, like wage laws or discrimination
laws, or if they change the terms and conditions of employment in an extreme way and the employee cannot comply because of economic, health or family reasons.
So, although there are no guarantees, if you want to maintain some chance that UI benefits, you would want to make them terminate you. That said, they are offering you some extra money to resign, so that, and not having to put that you were terminated on applications might be worth it to you. That is up to you.
Please let me know if you need any clarfication. I would be glad to assist you further if I can.