Yes that is a challenge !
OK, how to proceed…..
You have a choice…..
1. Rework the cable to create something that will work and be secure in theZIF socket
2. Rework the other end of the cable bu finding the landing points of the cable on the PCB before fitting a ZIF socket modification to the PCB. There are only a few conductors.
3. Strip the FPC insulation and solder a ZIF socket to them. Then use a new FPC between the new ZIF socket and destination ZIF socket
Option 1 will be worth a try but options 2 and 3 will still be possible if your efforts fail.
About stripping the FPC…..
1. It is not an easy task !
2. Remove only only one side of the insulation ! The FPC is two layers with adhesive holding them together.
3. Use a very sharp scalpel to carefully cut away the insulation and peel it away from the other side of insulation.
4. Adhesive residue may remain after cutting away the insulation. Very carefully clean the adhesive off of the copper conductors with white spirit (terpentine) and allow to dry. Do not remove the adhesive that is holding the copper conductors to the other insulation layer ! this is challenging !
5. Attach layers of Kapton tape or similar shiny, non stretch, ‘hard’ tape to the insulated side of the FPC to create the correct thickness for an easy, but not too loose, fit in the ZIF socket
6. Very carefully insert the FPC into the ZIF socket. Be aware that the copper conductors can peel away from the insulation layer and ‘crumple up’ as the cable is inserted. Care and patience is needed.
7. Apply any locking bar that the ZIF socket uses to hold the cable in place.
8. Apply some acid free RTV to the FPC and ZIF socket to reinforce the mechanical fixing between the two. Hot melt glue is not recommended.
If you are working with a non ZIF socket that requires the FPC to be forced into sprung contacts, the chances of success are slim to nil as the copper conductors are pushed away by the sprung contacts as you try to insert the FPC

Sometimes a removable thin polyester sheet may be used to protect the copper conductors during insertion and then slid out carefully afterwards. Overhead projector plastic (acetate) sheets work well in this roll as they are thin, hard and shiny.
Fraser