Can Vds ever becomes negative in mosfet?
Yes, your understanding is correct. In reality, a MOSFET is a four-terminal device. The body is not necessarily connected to the source. For the planar MOSFETs used in VLSI design the source and drain are physically the same kind of structure.

So, the source of the NMOS transistor is the terminal with the lower voltage, out of the two terminals that could be either source or drain. This behavior is necessary for bidirectional analog multiplexers that use MOS pass transistors.

That means that the answer to your question is no, \$V_{DS}\$ cannot be negative, because the more negative terminal is always the source.