Can you complete Hitman: Absolution without negative points?
Solution 1:
The following answer is based on my experience with the Hard difficulty, and only the Hard difficulty.
The only way I know of, where you can beat a level without any negative points, would be to kill your target without interacting with anybody in any way. Which means: Do not subdue or kill anybody except for your target.
However, if you manage to hide the body of a non-target after subduing or silently killing him, the points you get from hiding the body completely negates the points you lost from subduing him.
Keep in mind, though, that killing a civilian removes an additional 6000 points, which cannot completely be nullified.
On a semi-related note: Hiding a body does not kill, regardless of the hiding spot. So after you subdue someone, you can push his body off a cliff to hide the body and he will not die.