Ive been trying to find a way to create a negative light source in cycles for a while now.
Simply put I want a mesh object or light object to reduce the amount of light in a area similar to the “Negative” function in the good old blender render 
I know that the Holdout surface works a bit like this but I don’t think it works to put a Holdout surface to a lamp and if I put it on a mesh then the negative light isn’t fading on the sides or anything like that, and you can’t put different values on the Holdout surface either.
Holdout just modify alpha color component to make “holes” in image for later postprocessing.
I do not see any clamp or negative test in Cycles main loop, try to create emission source and modify it output later with math node.
Thanks storm_st I managed to do it with the math node as you suggested. Here is the setup I used
If you can’t see the text here is what the first node looks like
Its a Subtract node added by Convertor -> Math. Change the first value to 0 and the second value to whatever
negative light value you want. Then connect the output to the Emission strength input.