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Ah, another flamewar topic!
If I understand it right, an unnoticed corona discharge during the
disassembly of the capacitor causes the metal plates to coat the
dielectric with ions. The edges of the plates act as "charge spray
needles", the same as the combs on a VandeGraaff.
Why would the edges of the plates start spraying charges into the air? As
the plates are separated, the capacitance drops to a low value. The
charge on the plates doesn't change, and by V = Q/C it causes the
potential difference to go through the roof. With the edges of the metal
parts being adjacent, an air-discharge is guaranteed. The edges of the
two plates spew out charge, but because they are separated by the
dielectric, the charged air plasters itself all over the surface of the
dielectric. The dielectric now behaves as a charged capacitor, with
surface ions being the "charged plates."