Spark will continue, but as coil energy is depleted it goes out. At the start of ignition when IGBT turns off, the coil voltage increases 4-20kV, when ionization happens, voltage at plug is ~ 80V. That is why it last for a few ms. The first strike has most energy, does most good for ignition. Multi-spark is advantage, COP coils have low inductance, charge quickly. Getting rid of rotor gap halves lost energy. That gives time saving too.
Turning IGBT "on", stops spark, and starts charging coil. The time it takes, is based on supply voltage, inductance, and current peak desired. Current limit circuits, and "on" time achieve desired current peak. 4A for TFI coil, is good starting point for peak current. Ballast resistors work too, but waste, without active dwell control. HEI coils have low primary resistance, without proper dwell, or current control, they can fail in a very short time. It is not coils fault, it is improper use. Put one on a mopar box without proper ballast, will likely fail coil and box.
I measure current by inserting a 0.1 Ohm or less resistance in ground circuit of IGBT, I = V/R. Use high voltage probe,1kV or more to view coil primary voltage with scope.
I think there is much on coil testing in the COP Development post. Learning how to control IGBT drive signal timing is the most important part in ignition system development work.
What uC are you using?
