Was about to submit my 2 weeks, manager proposed a lay off if I stay for another month. What needs to happen to make sure they do what they say they will do?

If I quit I’ll receive nothing. Severance package for lay offs could amount to $28k for me. I’m in the middle of a project and he wants me to stay for a month working on it. My time is flexible so staying is not an issue but I don’t want to get screwed by finishing the project that month and not getting my 28k. Is there a “lay off agreement” to be signed and if so, can they sign it and back out of it after I have stayed for the additional month? Thank you in advance. This is my first time leaving a company. Edit: the same way an offer letter can be retracted after signed, a severance agreement can be pulled after signatures?