Failure of Metallized Film Capacitors
Self healing caps are typically used for direct connection to mains supplies. Mains can often have 1500V or more spikes appearing on the conductors briefly, due to switching events or lightning strikes in the supply network.

In an MFC that is designed for self healing (not all are), the metal film is patterned into a mesh of squares with fine connections between them. These fine connections behave as weak links, or fuses. If an overvoltage punctures the insulator between two squares, the fuses to those squares vapourise. (How they chose manufacturing parameters so that the metal vapour doesn't condense to form a bridge between the films, I don't know, but I guess that's why they make capacitors, and I don't). 

Now with the links gone, the punctured region is isolated from the rest of the capacitor. The capacitance will have dropped slightly, but with the electrodes made from hundreds of squares, it's a tiny fraction of its total capacitance. This can be repeated, and a capacitor exposed to many overvoltage incidents can lose a significant part of its capacitance evnetually.