They may want to sell for $0.01, but they may not be able to and you won't be able to buy. See also: articles of incorporation, minutes & bylaws, shareholder agreements.
Of course. But in many cases they will. And even in cases where there are restrictions....there are often things that can be done. But that's not really the point.
My point is calling something illiquid worth "nil" is often silly. Maybe don't consider it worth its face value. Certainly don't go spending money you don't have yet. But automatically writing everything down to zero is dumb.