B777-200
Flight Crew Air Transport Pilot (ATP)
Flight Crew Total 904
Distraction; Human-Machine Interface
Aircraft Equipment Problem Critical
Air Traffic Control Provided Assistance; Aircraft Equipment Problem Dissipated; Flight Crew Requested ATC Assistance / Clarification; General Declared Emergency
Aircraft
We were level at 5;000 feet approaching ARSOT intersection.  We were cleared the ILS11.  They were reporting a 4 KTS tailwind and the airport had just changed from Runway 29 to Runway 11.  As we were turning to intercept the localizer the autopilot kicked off and the airplane yawed.  We identified the right engine failing.  The engine instruments were winding down and we had a right engine fail EICAS message.  We were at Flaps 1 and at 210 KTS.  The Captain took control of the airplane and called for the checklist.  I pulled up the Right Engine Fail checklist.  We started doing the immediate action items.  We did the autothrottle arm switch - right - confirm- off.   As we were getting to retarding the throttle the auto-relight [system] restarted the engine; the throttle was advancing and the engine had restarted.  We abandoned the right engine fail checklist and reconnected the right autothrottle arm switch.  At this time both engines were running and the Captain made the decision to continue the approach.  We declared an emergency; told ATC that we had lost an engine but had restarted it and asked to be met by ARFF.  Now we noticed we had a TAC [Thrust Asymmetry Compensation] Failure checklist to complete.  We accomplished that checklist and the TAC re-engaged.  We also had a status message R Engine Control.  We finished the descent checklist (we still had not gone through transition) and configured the airplane for landing.  We discussed changing the flap setting to 25 but decided with the tailwind 30 would be better.  We accomplished the before landing checklist.  We landed uneventfully and taxied to the gate.
While configuring for approach the flight crew of a B777-200 suffered a right engine failure.  Before they could complete the engine fail checklist the auto-relight system restarted the engine and the flight crew continued to land after declaring an emergency and requesting CFR in case the situation deteriorated.