It's commonly stated around here that VCs expect 9/10 of their companies to fail. So yeah, theres a good chance they are worthless. I think lottery tickets are a better metaphor, as they can be worth something. Wastepaper is hyperbole.
I don't think its foolish to ask for more equity as compensation, though obviously I don't know anything about your performance or current compensation. :) In fact, I would recommend negotiating better. Sibling comment has good advice on preparation. I would add talk to an accountant about tax considerations, and talk to a lawyer about the legal aspects of it. The last time I talked to a lawyer, it was ~$120, and that was a somewhat complicated situation. If you don't want to spend that much money on something that could be worth thousands or millions, well... You might end up like a lot of the other posters in this thread, and that is sad.
Seriously, a number of the posts in this thread likely wouldnt have happened, or could likely be resolved had the victim talked to a lawyer. Its like if you were robbed; you call the cops. Some people are saying its not worth it, it costs too much money, etc. If you arent going to call the cops, you can be robbed with impunity. It also means the thieves might grow bold, causing more headaches for the rest of us.
A number of people have said that the company/management told them that talking to a lawyer would be a waste. This is the thief telling you not to call the cops. You wouldn't take legal advice from a thief, right?? At least one person stated that the company "made" them sign something. This is the thief saying you "have" to give them something. If you sign something saying they can take whats yours, then they can. So talk to a lawyer before agreeing. The more upset they get, the more pressure they apply; the more likely it is that you need to talk to a lawyer.
Please, everyone, stand up for yourselves and get a lawyer. There are so many sad stories in this thread. The idea that people making 6 figures, with equity that could be worth that much or more can't spend ~$100 bucks to protect themselves!? It's appalling. Saying that it costs too much, not worth it, it wont matter anyway; that is like Stockholm Syndrome. Ok, that was hyperbole, but seriously, protect yourself.
Edit: EVIDENCE! The cops can't do anything without evidence, neither can the courts. Well, your testimony is worth something, but its better to get it in writing. Consult your local laws, or a lawyer regarding things like audio recordings, recording phone calls, etc.