On running the modflow model, the volumteric budget mentions the term recharge out. Does this recharge out look after the negative recharge? Does this mean modflow can handle negative/zero recharge Or capillary flux?
Yes, you can input a negative value for recharge but why not use evapotranspiration or just evaporation? I am aware of negative recharge occurring when the aridity if an area allows for evaporation from a shallow water table - essentially a negative recharge. But more accurate to model as evaporation.
As answered above there is no reason that you cannot add a negative recharge to the upper cells of the model.
However, in most common situations there is a specific package for that in MODFLOW, the well(s) and evapotranspiration packages are just two examples. But, there is much more. This is not only recommended but necessary to simulate the associated physical processes, while just specifying negative recharge will not account for the specificity of the underlying physics.
Another advantage of using the supported packages is to account for each individual component when reporting the mass balance at the end of each time step.