It seems to me that GM is probably "insolvent" already, in the sense that the value of its liabilities exceeds the value of its assets.*
But if it is insolvent, how come its equity is still trading at a positive number? Easy. Think of the equity as an out-of-the-money option--worth something as a lottery ticket, even if worth nothing at the moment.
Here's an example. LittleCo has assets of $80 and liabilities of $100. So, insolvent. If LittleCo liquidates today, its creditors get 80 cents on the dollar and the equity gets bubkas. But LittleCo has a chance to invest all $80 in a new project which will yield (a) $160 or (b) $80, with a 50 percent chance of each. This pencils out right: 0.5(160)+0.5(0)=80.
But from the standpoint of equity, there is the chance that something may turn up. How to measure the chance? Value the payoffs to equity. That would be: 0.5(160-100)+0.5(0)=30. So equity is worth $30, even though the company is insolvent. By the way, to double-check, figure the current market value of debt. The value is 0.5(100)+0.5(80)=50. Again, this pencils out right: $50+$30 = $80, so everything checks.
By the way, this is the same logic that leads to the conclusion that a homeowner whose mortgage is bigger than his house may nonetheless keep paying (link).
*In the bulldog of edition of this publication, I said it exactly backwarads. D'oh, no wonder my students don't understand me. And thanks, Taxmom.