HI!

It certainly should NOT be supplying power with the system shut
down.

Whoa there...some desktop systems *do* in fact keep their USB ports powered
when the power is "off". This is probably perfectly normal and nothing to be
worried about.

Something is very wrong there. Dunno about milliamperes but it is 5V,
IIRC.

The official spec for USB is 500mA at 5 volts DC. Most ports will stand
more. If your computer keeps the ports energized when turned "off", you may
not want to put a heavy load on them, as they may be getting power from the
+5 volt standby supply.

William