Can I leave it unconnected pins in the level shifter?
This is from the TXS0108E datasheet:



it shows the input detection circuitry. Rpua and Rpub are 40k

The real question is: what happens if the input drivers are left floating? 

Nothing, the chip already has internal pull ups. This also means there would need to be a fairly high noise source current on the pins to get the signal to transition, which is highly, highly, unlikely  and would transitions would only happen in worst case conditions. (you'd have to turn that floating pin into an antenna, and get more than ~100uA through the antenna to create a voltage edge transition the first port to get a transition on the other port). I would suggest that the inputs can be left floating and not have any serious problems.