MOS current mirror region of operation
The drain voltage of M2 "can" be of any value but it's only useful as a controlled current sink when Vgs is high enough that the pair functions as a good current mirror. 

The compliance voltage for saturation (where the current is mostly constant) is:

Vout > Vgs - Vt  so if you are operating M1 at a current that creates a Vgs only slightly above Vt (in other words, a very low bias current) you can have Vout almost zero and still get constant current. 

Here you can see a current mirror compared at 100uA/1mA/10mA and the behavior as Vds increases from 0V to a few hundred mV. At higher currents, the compliance range of voltage is less (you need more Vds to maintain a constant current). Vgs is about 1.41V to 1.73V in this simulation, depending on current.