This strikes me as the sort of thing I should have prepared in advance, just in case. Should I ever be fired for cause I expect I'll be too upset to think about what to ask for and how to say it so I better work out the basics now.
Believe it or not, you have the power in that situation. That's why they want you to sign it right away - right now you're emotionally distressed and thus gullible.
So that's how you prepare yourself: remember that if this ever happens, DON'T SIGN ANYTHING until you calm down. It's okay if that takes several days.
(This is from experience at past employers, I don't speak for my current employer, I haven't actually been fired but I've been on the other side, I am not a lawyer, This does not constitute legal advice, blah blah.)
Another thing that IMO ultimately in the long term should be fixed. Not being hired because you criticized a previous employer is worse than being fired for criticizing the current one IMO.
Remember that a severance offer is a starting point. If the only thing you want to add in negotiation is something that doesn't cost the company money-- good reference and a revision of the record to say you left voluntarily-- they'll usually give it, unless you did something illegal and they're afraid to give you a good referral for liability reasons.
Getting fired is something that happens to a lot of good people... for all kinds of bizarre and stupid reasons. I wouldn't mention it, as a general policy, but I really doubt that he couldn't find a job because he was fired. He probably became insecure and that did him in. He probably was also too loose-lipped about his feelings toward the previous employer, which is even more damaging because even if a past employer is terrible, one shouldn't let it on in an interview.
"Persona non grata" in the tech community after a job goes bad... that's just bizarre. In my experience, people familiar with startups are the most forgiving of jobs that went bad or ended suddenly, for the obvious reason that a lot of startups fail.