You can always turn it down. Contracts have whats called consideration.
I've seen companies try to get away with NCA/NDA by tying severance to signing one. I would have to be truly desperate to take the money over the health of my career, yet that is exactly what a lot of companies rely on.
In the US, I have never seen a severence agreement that did not include confidentiality provisions. However (IMO) the inclusion of non-compete provisions has become more common across all levels of employment and all job categories. The vast majority of US workers will sign these agreements. That cultural trend makes it (a) easier for employers' legal counsel to manage any issues raised by the minority and (b) more difficult, if not impossible, for the minority to negotiate.
Yeah, having been in that situation, my thought is that negotiation is worth a go, but the real response is having a good BATNA. Yet another reason to have savings at the 6-months-of-expenses level.
I've seen companies try to get away with NCA/NDA by tying severance to signing one. I would have to be truly desperate to take the money over the health of my career, yet that is exactly what a lot of companies rely on.