Sometimes it happens that the charging cord gets stuck, and you cannot remove it either from the charging station or from the car. It's known to occur with J1772 charging stations. There's a latch on some stations that can get stuck, preventing the cord from being removed.
I've encountered this problem with certain ChargePoint stations. Even though authenticated with the station, with a message displayed to remove the cord and start charging, you cannot pull the cord out. No matter how you pull and yank, the cord won't budge. I'm told the older CT2000 stations can fail this way, and that the newer CT4000 stations do not.
Some electric cars also have a latch that can prevent cord removal. The idea is preventing other people from unplugging your car. But some cars have a bug that keeps the latch engaged even when it's the owner who is trying to get the cord disconnected so they can drive away.
The workaround is to use a long thin stiff thing, like a long-bladed screwdriver, to reach in and disengage the latch. Here's the effect you're trying to achieve:
This screen shot comes from a video: https://www.youtube.com/watch?v=k5ck2yzTc10
You are probably thinking I'm nuts to suggest sticking a metal thing inside an active power outlet. Look carefully, though, at the physical structure of the plug and socket. The location of the active electrical contacts is well protected from the location of the latch. It's safe.