I used to travel on 777’s to and from Asia. It was always in the back of my mind what would happen if 1 of the 2 engines failed
The crew would simply land at the nearest suitable airport.
So, what would happen is the crew would divert to the nearest suitable alternative as specified in the release. That’s it.
I'm a 777 pilot, the plane flies fine on one engine. Look up a picture of the GE-90 engines, they're huge and put out a lot of power. You'd divert to the alternate for that portion of the flight. There are multiple alternates going to and from Asia from the U.S. Anchorage, Adak, Shemya, Midway island, Petropavlovsk-Kamchatsky and multiple others as you get over Japan.
A big part of the certification for two engine jetliners to cross the oceans was making sure they're capable of flying a long way on one engine. Losing an engine over the ocean was a big part of the design consideration and there are an unbelievable number of redundancies built into them.
That covered by ETOPS
Engines Turn or Passengers Swim!