Since we are in the discussion of departing engines should we include the American Airlines DC-10 in Chicago where the ATC stated American you lost one engine but the crew couldn't understand they meant it literally?
Same has happened many other times (lavatory ice events, fuse pins etc.)
The crew simply fly how the aircraft behaves, often lower drag than with a dead engine. What consequential damage occurs to the aircraft has been the key link to a successful landing.