Originally Posted by JulieS

I'm not sure where you got that definition of Total Slack. Total slack is the difference between late start and start or late finish and finish. From help:

The Total Slack field contains the time a task's finish date can be delayed without delaying the project's finish date.

If a task's only successor is SS then delays to the end of the task have no effect unless the finish of the predecessor task goes past the successor. However, the task may very well have zero total slack because any change to its start will change the successor start.