I have bought a cheap soldering iron. It seems to work fine.
Out of curiosity I tested the metal enclosure (and thus also the tip) with an electric tester and it lit up. Then I tested it with a multi-meter and it shows about 120V with respect to one of the mains and 0 with respect to the other. Mains is 220V where I live.
Then I tested the resistance between the metal enclosure end both of the power socket pins (it has only two pins, no ground wires.) It shows infinity. The metal enclosure gave no shock while connected, though I was heavily isolated from the ground.
I am interested in knowing what is happening.
My guess is capacitive coupling. Will I get a shock if I am somehow connected to the ground? Is the soldering iron ESD safe? If I ground the tip (and thus also the enclosure,) won't it trigger the ground fault detector?