There must be a name for it. 'Ritstrekkers' perhaps? Those metal lips with which you move the 'zipper' of a zipper up and down - or from left to right or vice versa.
So those things are already broken.
Repairing the case with a paper clip is a solution. A large paper clip as a zip puller is certainly very practical for motorcyclists with cold hands.
But Macna / Splashdesign has a much nicer solution for broken zips: Replacement Pullers. For only 4 euros 95 you have 4 fresh pullers and your zipper will look clean and sparkling again.
A perfect invention
www.splash design.com / Clothing /MACNA/ Accessory