App note from Vishay about self recovery of metalized film caps. Link here (PDF)
Voltage proof tests, also called “high pot” tests, are used to check if a capacitor has a breakdown failure mode occurring at a certain test voltage. The detection of breakdown is done by a current detection, specified if exceeding a certain limit (cut off current).
For all capacitor technologies that do not have the ability to recover after a partial breakdown, the current flow is continuous at the moment of a breakdown.
However metalized film capacitors have the property to recover after an instantaneous breakdown (partial breakdown) due to the fact that the metalized electrodes (capacitor plates) act as a fuse. For fusing a small current is needed, but is not continuous.
This effect is defined as “self healing” and not as breakdown.