Is it possible to have negative bond orders? In the MO theory, is it possible to have a molecule with bond order less than 0? The least bond order I have come across as of now is 0 (for di-atomic noble gases), indicating that the molecule cannot exist and the atoms get pulled apart.

Is it possible to create a scenario (at least theoretically) where we deal with a negative bond order by manipulating the system's conditions or any of that sort?
No, it's not possible, theoretically either.

If you see the Molecular orbital theory, maximum number of anti bonding electrons = number of bonding electrons.

And bond order is (Number of bonding electrons - number of anti bonding electron)/2 

So, the minimum value that you can get is 0 and not negative, as anti bonding electrons can't exceed the number of bonding electrons.