NMOS saturation mode: why is there no channel?
At onset of saturation, inversion charge near drain decreases until it becomes zero, close to drain region. VD at which this happens is called pinchoff and
drain current starts to saturate. At saturation regime (VD > VD-sat), pinchoff moves towards source leaving behind a depleted region; inversion charge drifts down conducting channel and is then injected into depletion region.
ID will essentially remain constant because inside channel potential is fixed at VD-sat.

Please note that this is kind of "first-order" behavior of the MOS transistor, in reality the drain current in saturation regime is not constant and is affected by many other phenomena e.g. channel length modulation, velocity saturation, etc.