You're just an employee, if you feel your company is going under, find other employment. Once you find another offer, they'll either offer you a share of the company to stay, or you can leave.
This is probably true -- though I've been in situations like that before (swap shares for money) and never take them as I just don't think that type of very passive "threat" (for lack of a better term) is ever fruitful. But, on the other hand, I don't have a ton of business experience, so maybe it would work out. Do you have any experience in those situations? Staying after discussing leaving?
Many articles have been written about this: don't ever accept a counteroffer (google "counteroffer" to find them). It is generally just a way to delay your departure until they can quietly find your replacement, at which point they will fire you. And you don't want to work at a company that only treats you fairly when you threaten them.
If you discuss leaving, make sure to look sincere in the discussion. This means steer the conversation so it shows how you are worried about your future financially and therefore you need to be proactive (have them empathize with you and see you as a human, not an employee).
In case you decide to return to the company, this way you will have retained some of their respect.
I'm not talking shares for money: I'm talking about they pony up a share and money like they're getting if they want you to suffer through the broken/poor part of the companies existence.
If you find another position, take it. Don't try to use quitting as leverage to make things happen - even if you stay on, your actions will always be there, lurking in the background.