17:55 Dec 2, 2011 

Drawstrings are always threaded and may or may not be removable (that depends on whether they are stitched in at some point or joined at the ends to make a continuous loop). Dustbin bags also come in a variety of shapes and forms. The expensive ones have "liens coulissants", which are threaded in a continuous loop. The cheaper ones with "liens" have a thin strip of plastic tape at the bottom, which you rip off to tie the bag. Of course, these are not a fashion statements and you would only wear them if desperate; however the linguistic principle seems to be the same.

16:56 Dec 2, 2011 

How about 'fixed or removable drawstrings'?

08:47 Dec 2, 2011 

As far as I know there are two types of drawstrings used in clothing: one is not anchored and can be pulled all the way through the casing; the other is sewn in at certain points and is only used to tighten the front of the garment. I don't know if this is the difference being referred to here, but it is a possibility. I don't know an English term to differentiate these two types of drawstring, I'm afraid, but it might help you in your research.