[PaulE]

I've seen the official name for that as both 'tension rope' and "fold placer string." It runs across the top between the headliner and the top and its purpose is to help the top fold properly when its going down. In your picture it looks like it is connected to the side rail of the top frame, which is correct, and it should be connected on the other side the same way, with small Philips screws and maybe a plastic ear thing. One of my plastic ears broke, so I replaced them both with small plastic washers and it has worked fine like that for years. There is supposed to be a piece of elastic in the center section that the strings from both sides connect to, but I have never gone inside to look. From your picture I think the elastic or string somewhere in the middle between the top and the headliner has just broken. I can't be sure of the part number for the 986, it might be 986-561-921-00 for the 987 it is 987-561-773-01. Here is another thread on Renntech I found when I had an issue with mine.

Just saw Husker Boxster's comment. My car is a 2003 986 and it has that string, maybe the earlier 986s don't have them. Well now you have the 987 part number!