If the engine continued to run without the electrical system (i.e. the lanyard was removed), the fuel has to be getting ignited from somewhere. Likely you have some carbon deposits in the combustion chamber that are getting hot enough to ignite the fuel. Carbon deposits are very common in two stroke engines. In addition to rebuilding the carbs, I'd suggest decarboning the engine using your favorite method. You'll likely need to replace the plugs afterward, but you should do that annually anyway.
Air leaks anywhere into the motor case will cause a lean condition.
Check to see if the throttle cable has slack in it when it is at rest. The most common problem of a runaway idle is that the last guy did not install the throttle cable with enough slack in it. But that only applies to one that has had work done to the carbs or to the cables.
Sometimes richening the low speed adjusters will stop this runaway condition, unless the jets or filters inside the carbs are clogged up.
They run away because they are too lean for the amount of fuel being put into the motor. They get too mch air, and not enough fuel.951 engines will run away even without air leaks or lean condition. Check the archives for Bill86e's instructions on setting the idle on 951 engines. They will run away if the idle speed is set too high. You must have slack in the throttle cable at the idle position, and to set the on-hose idle speed to 2800 rpm, 1400 or so in the water.
Ever hear the term "Glowplugging" the tip of the sparkplug gets red hot and ignites the fuel without electrical imput to the sparkplug.
This happens when the motor runs too lean of an air/fuel mixture. Too much air, not enough fuel. Fuel keeps the combustion temps within a certain safe range. Take away the fuel just a little bit and you have a glowplugging motor that revs to the moon !