FDR will tell you it ran out of fuel, when, and maybe some info on the descent, but nothing about WHY unless it captured some sort of failure,
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Remember the Silk Air MI 185 Boeing 737 suicide crash? The investigation found that the two cockpit FDR circuit breakers had been pulled just prior the aircraft being pushed over into its dive. That meant no info after that was available to investigators. The CVR circuit breaker had also been pulled a few minutes earlier which is why the only CVR info that was available was the period before the CB were actuated by someone. If someone in the 777 went to the trouble of switching off the transponder and ACARS, chances are the same person may have tried to hide more vital information by disabling the CVR and FDR by some means (circuit breakers in the 777?)