(Please note that I am not a lawyer. If in doubt, I would recommend contacting a legal professional. You also omit the country so it is hard to give specifics. I will assume a western, English speaking country like the USA, UK or Australia.)
Have you signed the first document (contract)? If so, in theory, it becomes a legally binding contract between you and your organization. However, in practice, the organization is likely to do as it pleases. If you have not signed the first contract, the company can withdraw it and present a new contract.
If you have signed the first contract and you fight or get a lawyer involved, chances are the organization will either (1) terminate your employment immediately and/or (2) pay you the statutory minimums. These redundancy contracts usually pay more than the minimum and lawyers are expensive. Therefore, it is probably best to take what you can and put your energy into finding new employment. Look at it from the organization's point of view: paying you a few extra week's salary is much cheaper than a court case or bad press.
A better idea is to talk to someone in HR in a different organization. They can give you insight into the process and common practice. Also be aware that no one should be pressured into signing. The organization can ask for signed contracts by a date but this should be at least a few days to give people time to think and get independent advice.
Note that, if you are being exploited, the best thing you can do is talk to others in the same situation. One person can be ignored. A whole team or department creates a headache. The contract usually states that you cannot share the dollar amounts but you can ask if others are happy.