I am sorry this happened to you. Don’t panic. Don’t go into depression. You don’t have to sign to get your pay or vacation. That’s yours. You probably have to sign to get the severance. The fact that they are being dishonest with you about this worries me but there ain’t a whole lot you can do about it. If you take the severance you may not get UNenjoyment benefits which may last 2 years. Keep the form as evidence they offered to let you quit. You probably need the money more than giving it to a lawyer. The lawyer is the last option. One last thing. No matter what happens - DON’T THREATEN THEM. Even if they make you very angry. Don’t look back. Look ahead. If you need any support FReepmail me. I’ve traveled a similar road.
God bless you and thanks.