That's not at all how it works! The cam didn't break, the chain did. If you suddenly removed the cam, then yes the springs would instantly close all the valves, but that's not what happened. Instead, the chain stopped turning the cam. Even if the spring force of the valves could turn a cam (it really can't, let alone quickly), then you'd still have the problem that some would be closed (safe), and some would be open (big problem). There's no position to turn the cam to that has all the valves closed.
You have damaged valves, and may even have damaged pistons. Get/rent a borescope and have a look into each cylinder.