I've stuck it out to the very end a couple times. Once I was the last guy to lock the doors and walk away, after the CEO, after all the management senior to me. After the cleaning crew.
It really comes down to what you can afford. You've stated (obliquely) that your pay is being reduced. Can you afford to stick it out at the reduced pay? What is your opportunity cost for staying, do you think you can get a job at Square or some other too good to pass up opportunity?
Can you go a month without pay when shop closes up? Can you go three?
Some things to keep in mind:
Sometimes when companies are in trouble they get bought by other companies. This doesn't mean your options will be worth anything but you will have gone through an acquisition which can be a valuable experience.
Sometimes they get shut down or liquidated: Still valuable experience (just once though, please.)
Sometimes lightning strikes and your startup comes roaring back to life. This one really depends on the team and your leadership, not to mention whether there was anything to begin with. If the team is broken and has lost hope then it's less likely anyone will find that inspiration that can change everything. If people still have fighting spirit you might have a chance.
I'm sure your CEO is wracking his brain trying to figure it out. His job is the worst job you can have right now. While you see a company failing, he sees himself failing. The simple fact is that most startups fail. They are experiments to begin with. Learn what you can.
The thing is, everyone who sticks around will have gone through something very difficult together, regardless of the outcome. Doing so makes those relationships valuable and long-lasting. A lot of "success" comes from solid relationships with people you can trust.
Tech startups are hiring like crazy right now. Definitely find out how much time is left. Time is the only thing in life you can't get more of but that doesn't mean you shouldn't choose to do something really hard once in a while. If the remaining runway is pretty short then it's unlikely you'll miss out on the rest of the current tech boom.
So, figure out how much time is left before the company ends then weigh the opportunity cost of staying versus where you might land if you go.
Oh and if someone offers you a job at something like Square that has the potential to change the course of your life through the amazing people you'll get to work with, the network you'll build and/or massive potential financial opportunity: TAKE THE JOB.