and scaling them along the y axis to zero did no good. So How can we cut a hole through a subdivisioned mesh without actually applying the modifiers? I know disabling the boolean modifier would give a nice hole in the render but what if we have to do some editing with the part, like adding a drawer object(particularly in this case)?
You can use the Inset tool. That way you can keep the topology as quads.
Select the faces where you need the cut, press I to activate the inset tool, and then by dragging the mouse you can determine the size of the hole.
After just extrude (E) and delete the faces as needed.