In our post "Setup and hold - origin", we discussed that every device captures data within a certain window known as "setup + hold window". During this time, data must be held stable so that it can be captured properly. Outside this window, data is allowed to toggle.
Figure above shows "setup+hold window". This window is characterized by the setup and hold times of the device. The width of this window is essentially the sum of setup time and hold time. Thus, if the sum of setup and hold time is positive, it means there is a finite window wherein the device is allowed to capture the data. On the other hand, a negative sum of setup time and hold time indicates that the width of this window is negative. In other words, the window does not exist. So, a negative setup and hold time implies that the device cannot capture the data at all!!
Thus, for a functional device, we always need the sum of setup and hold times to be positive. :-)