Only time it would expire is after you have already taken an "end-of-course" stage check for a particular course of training. The end of course certificate of completion is only valid for 60 days from the date of completion of the end-of-course. If you don't take your FAA checkride within those 60days after your EOC, you simply just have to take another EOC and receive a new grad certificate.
Different schools will have different procedures for "terminating" a student's training prior to completion of the EOC depending on what that schools individual FAA approved policies are. Generally done in a letter to the school from the student or in a form as mentioned earlier. That way it's in writing just in case little johnny doesn't tell his parents that he's terminated training and Johnny's parents call the school three or four years down the line wondering where all their money has been going and why Johnny still has not soloed.