The leakage current is not always "leakage" either.
Electrolytic capacitors are what they say, they have electrolyte inside them. The dielectric is actually an insulating layer formed on the surface of the aluminum foil by electrolysis.
Old capacitors that have not been used for a long time may need "forming" to rebuild the insulating layer. This forming process will consume a certain amount of current while it is occurring.
Furthermore, until the forming is complete, the capacitor will not withstand the full working voltage, and may fail if you increase the voltage prematurely.
Therefore, old electrolytics need to be handled with care, and if they need reforming, this should be done in the appropriate way before trying to test them.