The passengers would be unaware only if the engine failure occurred near the destination. Pilots don't just keep flying for hours with an engine failure if they have any alternative places to land.
Funnily enough I was searching about for info on B772 single engine range and found this anecdote that contradicts you.
>Just as a practical example of reduced range with an engine out, We departed Santiago, Chile in a 747 freighter with enough fuel to reach Miami. During the climb out we lost an engine. We elected to continue rather than dump fuel and return. However, because we could not reach our intended cruising altitude, the increased fuel burn meant we only had enough fuel to reach Panama City, Panama
Almost definitely not, but it still shows that pilots aren't too concerned about engine outs to the point where it's an automatic mayday, especially on a four engined planes. I wouldn't have shared the anecdote if it hadn't violated my preconceptions.
As with anything, there always are exceptions. In this case Smartwings flight QS-1125: the pilot in command ignored an engine failure and went on to land on the original destination instead of landing at the closest suitable airport.
