Chosen Solution

I was replacing a shattered screen on my iPhone 6. I had put the entire phone back together and reassembled when I noticed the top of the phone was getting very hot. This was caused by the camera assembly shorting-a topic unrelated to the question at hand. What is currently causing me problems is that when I went to open the phone back up, I removed all the ribbon cables again, and when I came to one of the cables for the LCD, the end that slots into the socket on the logic board separated from the ribbon cable, so it is now stuck in the socket and I am not sure how to remove.

You should be able to remove it with some pointy tweezers. You have to work carefully, ideally with magnification, so that you don’t poke any tiny surface mount components near the connector and potentially damage or tear them off the logic board. You also want to avoid damaging the connector that’s supposed to stay on the logic board.