Hey, I have a 1970 El Camino with a 350 and the car started just stalling out today. Randomly it would cut out, not ever sputter or anything, just turn off, it would always start up though. When I got home, the key was on and the engine off because it had stalled and I noticed that one of the small wires coming off the coil was burning, smoking and melting the plastic off it. I looked and it didn't seem like it was touching anything else so i dont know what the problem could be. Anyone know what the problem could be?

The wire doesn't burn when the engine is running, just when the key is on all the way but the engine isn't running

Leaving the key on is not a good thing to do especially with a points system. If the points happen to be closed when the engine is not running and the key is on, you are shorting the ignition circuit to ground through the points and primary circuit of the coil. I would suspect that your points need to be filed if pitted or if fused you might have to replace them. It's possible to burnout the primary wires in the coil, damage the ignition resistor wire or wire between the negative terminal of the coil to the distributor.

WHICH "small wire" ?

There are only two other wires coming off the coil other than the one going to the distributor right? This wire goes right into the wiring harness, not sure where it leads though. Could this be the reason for the stalling?

IF the car still has it's original points type distributor AND/or the original resestive type feed wire from the bulkhead connector to the coil's + terminal, it sounds like maybe that section or resistive wire might be going bad.
Either that or it's carrying too much load caused by a possible bad coil or shorting to ground. OR has a loose connection possibly.

It was a fairly common thing for that resistive wire to go bad and have to be replaced with regular wire with a ballast resister in series.