vdsat negatif
As Vgs-Vt approaches zero, the device is no longer working in strong inversion, and a different set of rules occurs because the conduction is no longer dominated by drift. Using vdsat = vgs-vt is only valid in the strong inversion region.
The device goes thru a transition region (moderate inversion) where operation can be difficult to describe using a single simple equation suitable for hand calculations because the current is a combination of drift current and diffusion current.
Beyond the moderate inversion region, the device will enter weak inversion, where the dominant current is due to diffusion. In this region the equations become much like the equations for a bipolar transistor (do a search on Vittoz or EKV to find equations suitable for hand calculations for the operation in this region). In this region, the vds.sat can be on the order of 100mV or so. Below this voltage, the exponential equation for current vs vds that can be found in the above stated models will be most useful, above this voltage, you can use the channel length modulation as you would in strong inversion to describe the current vs drain voltage.