Which hazard generated by earthquakes can be destructive many hundreds of kilometers away from the epicenter?

I would say Fire is definitely a hazard by earthquakes

Hazard RiskThe chance that a natural hazard may take place.Natural HazardAny natural process that is a potential threat to human life and propertyConservative Plate MarginsOccurs when plates slide past each other in opposite directions, or in the same direction but at different speeds and often results in an earthquake.Constructive Plate MarginsWhere two plates are moving away from each other.Destructive Plate MarginsWhere two plates are moving towards each other.EarthquakeA sudden or violent movement within the Earth's crust followed by a series of shocks.Immediate ResponsesHow people react as the disaster happens and in the immediate aftermathLong Term ResponsesLater reactions that occur in the weeks, months and years after the eventMonitoringRecording physical changes, such as earthquake tremors around a volcano, to help forecast when and where a natural hazard might strike.Plate MarginThe margin or boundary between two tectonic plates.PlanningActions taken to allow communities to respond to natural disasters, through emergency evacuation plans, information management, communications and warning systems.PredictionAttempts to forecast when and where a natural hazard will strike, based on current knowledge.ProtectionActions taken before a hazard strikes to reduce its impact, such as educating people or improving building design.Primary EffectsThe initial impact of a natural event on people and property, caused directly by it.Secondary EffectsThe after-effects that occur as indirect impacts of a natural event, sometimes on a longer timescale.Tectonic HazardA natural hazard caused by movement of tectonic plates.Tectonic PlateHuge pieces of Earth's crust that cover its surface and fit together at their edges.VolcanoAn opening in the Earth's crust from which lava, ash and gases erupt.TsunamisLarge ocean waves caused by an underwater earthquake.Richter ScaleA scale that measures the largest ground movement that occurs during an earthquake.MagmaLiquid rock below the Earth's surface.AftershocksSmaller tremors occurring after an earthquake.LiquefactionThe loss of strength that can occur in the ground during earthquake shaking.RetrofittingThe addition of new technology to older buildings.Appropriate TechnologyTechnology designed with consideration of the community it is intended for.EpicenterThe point on the Earth's surface directly above the focus of an earthquakeBuilding CodeRegulations which state how a building should be constructed in order for it to be safe.Seismic ActivityMovement in the Earth's crust.Laser RangingUsing laser beams and mirrors to detect minute changes in the shape of the land.EvacuationMovement of people away from a place of danger to a place of safety.Storm SurgeAbnormal rise of the sea along a shore as the result of a storm.Physical EffectsThose affecting natural and built materials.
Hopes this helps you 
GOOD LUCK:)

Answerwill have thinner; have thicker oceanic sediments;