While trying to detach the cable, I pushed out the black part, which came out from the opposite side of where the cable enters the connector.
The cable was previously tightly clipped in place and came loose after the black part came out.
How do I re-attach the cable, or is the connector permanently broken?
Is there a name for this particular connector? There seems to be a few names, like zif, etc but I'm pretty sure mine isn't zif.