Not all, 10% of reserves. Once the run starts, no one wants to be the last 10% of people, cause that money doesn't exist.
I'm no expert, but it seems like the math is pretty simple, but banking is complicated and you may be right.
The way I see it, the bank is in FDIC custody because it's real reserves at market prices minus its liabilities (depositors money) is negative. There's no rescue from that. The bankruptcy court will sell its assets and distribute those to secured creditors and such and the uninsured depositors will get a haircut.