Is the current, Ids, through a MOSFET truly 0 when in the cutoff region?
It's all about \$I_{DSS}\$ so pick up a data sheet for a MOSFET and look up that term. It'll tell you something like: -

It's the drain current that flows when the gate and source are connected i.e. \$V_{GS}\$ = 0 volts. It's usually specified for a high-ish drain source voltage of maybe 10 volts to hundreds of volts.

Basically it's the leakage current of the channel.