Dave - your drawstring shower door may be a Singapore specific - I have never seen one here in the UK and can not see yours.
Drawstring curtains have a continuous loop of cord - the fixing is to one point so they open and close depending on which string is pulled - there's a return pulley at each end and the cord is joined in the middle - it never goes round a pulley.
First buy replacement cord - then arrange the cord around the pulleys and make a join - then fix the doors to the cord.
Good Luck..., April 2016