Someone I used to know,(TO), was a F/O on a Concorde that had a double engine failure mid Atlantic. One engine surged and coughed an inlet door out of the front and it went down the adjacent engine, The vibration was very high and both engines were shut down. The Mayday call to Shanwick was that they may not make Shannon. The reply was that they would alert the coastguard.
IIRC they restarted the engine with the lowest vibration and made it to Shannon.
I saw some photos of the engine that ate the door and the compressor was a mess.