Does linearity of a N-MOSFET continue for \$V_{DS}\$ below \$0V\$?
If by linear you mean drain current and voltage are linearly related, then:



You are in the linear operation region, upper right. Between the drain and source is an inversion layer, and this looks mostly like a resistor.

If \$V_{DS}\$ goes negative, then the current will go the other way. Since the gate voltage is (relatively) very high, there's nothing in the channel to make it significantly asymmetrical.

However, there is another effect in play. Notice that the drain in an N region, sitting in a P substrate. Smells like an NP junction diode. In fact, this is the infamous body diode. At \$V_{DS} = -50nV\$, this diode won't be conducting much. However, as \$V_{DS}\$ becomes more negative, the effect of this diode will become more significant, and the drain current-voltage relationship will become progressively less linear. That depletion region in the image will become progressively thinner, until it's not there at all, and you have forward-biased the diode completely, and \$V_{DS}\$ will be clamped at about \$-0.65V\$.