Once you've got the conductors exposed, you could just poke it into a card-edge connector (with the right spacing) and back it up with a piece of unplated PCB material, which would hold it in place.
I know, it's a klooge, but it would get the job done.
--- It's called "flexible flat conductor cable". If you're talking about the kind that has the conductors silk-screened on the carrier, like membrane switches, then you won't be able to solder to it, but if it's the other kind, with thin PC-like traces then you should be able to solder to it. I'd do the sanding before the cutting so you can expose as much of the conductor as you need to before you cut it. That way you wont have to deal with the edges when you sand the cable down. You may also just be able to melt the insulation over the conductors and then solder to the conductor without having to sand anything.
Another, much cleaner, way would be to cut the cable in the middle, put connectors on the ends, and then make a center section with matching connectors on it and ever how long you needed the extension to be between them.
What is the proper name for that clear flat cable that has flat metallic condictors 'printed' on it. I need to make or buy and extension for a four conductor one that connects two boards. Is it possible to cut it in the middle, lightly sand down to the conductors and solder a piece of ribbon cable to extend it?
"Copper on Kapton" is a common material used for "flex-circuits", such as the ones used to connect moving print-heads. I've also seen "silver on polyester", but the latter is much trouble (I.e. stay away, far-far away).
Should work in a pinch. I wouldn't do it for production, but for a fix or prototype it should work. I've done worse (e.g. patched SMT devices into it). The stuff acts much like copper on FR4 (but flexible, obviously).
I take it you're one offing. In which case it might be acceptable to use thin paper card with self adhesive copper track on it. You can design it however you want then, within the limits.
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