Very likely the simplest answer is: you have a broken switch. Maybe a critter crawled into the switch and created a resistive short across the open circuit of the switch. Maybe the switch just decided to give up it's ghost. These things happen. It might have smelled funny briefly but you didn't notice it.
Odds are with a 'real' (incandescent) bulb or some other load,the switch would burn up completely, but with a ultra low wattage LED, the resistive short isn't burning up. (Also with LED, likely the current draw is lower than the accuracy of your meter. Especially given that some cheaper / older meters struggle with the 'power factor' of some cheap LED/CFL bulbs.)
Go to your favorite local hardware store and buy a new switch. Cost you ~$3 and look up youtube videos on how to change out a switch. It's easy and safe if you cut the power first. Nice little skill to have. Good luck.
Also maybe the switch has a dimmer which never fully removes current, but assumes that for an incandescent a few mA won't light it up, whereas LED bulbs can generate light from this tiny bit.
Also in case OP doesn't watch a video, turn the breaker off and verify that the switch isn't hot (and verify that your tester really does identify something hot, like a plug outlet).
Good stuff. :)
Fuck yeah, I remember reading a cockroach shell will conduct electricity and they short out computers sometimes. If roaches or one roach dead on the contacts that would give a low current.
(post is archived)