How does a magnetic ballast (large inductor) stabilize a negative resistive circuit (such as a fluorescent light)?
I don't think that the fluorescent light is actually a negative resistor. If something actually has negative resistance, putting a positive voltage across it causes negative current flow, in other words, (conventional) current flows from the lower voltage to the higher voltage. A fluorescent light can't just do that by itself. Negative resistors are powered circuits that, when taken as a whole, appear to have negative resistance. A fluorescent light just has a resistance that drops as the amount of current through it increases. Its resistance is always positive. The purpose of the ballast is to resist the current briefly--until the next AC phase change--in order to limit the current flowing through the light.

This page has a schematic for a negative resistor. The more voltage you apply to the input, the more current flows from the negative resistor to the input. What's actually happening is that the op amp is producing a voltage at node B that exceeds the input voltage, causing current to flow to the input.