An aircraft is flying in cruise flight on a long distance flight. The autopilot is turned off. The only occupant of the aircraft is the pilot.
Suddenly that pilot dies, what will happen?
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It has happened before that the single pilot lost consciousness while flying. What then happened is that the plane just went on until out of fuel after which it will glide down and skid to a stop (pilot survived). This is assuming there is no obstacle in the way.
Another example is the cornfield bomber, a fighter pilot eject and the plane still under power just kept going in a straight line and "landed" in a field.
A more deadly example is the helios flight 522. A mistake in the pressure regulation setting let the plane become unpressurized while climbing to cruise altitude. Both pilots lost consciousness and the plane's autopilot followed its programmed path following the waypoints and ending up in a holding patter until it ran out of fuel and crashed into the ground.
Survival depends on luck with obstacles, whether the plane is properly trimmed and which order the engines flame out in, asymmetric flame-out may result in a spin.
Assuming no autopilot the plane will likely crash very soon as even if the airframe was trimmed at the time of pilot's death as there will be no mechanism correcting trimming on outer forces changes (turbulence, pressure change, etc.) Imagine a driver dying in a car - if the road is straight and wide, the car may go on for a while but as soon as there is just a small change in roads direction, uneven surface or even stronger wind, the car will crash quickly. Some planes may have features not directly tied to autopilot that correct piloting mistakes to some extent which may prolong the planes survival.
Also very important is what happens with the pilot's body. As long as the body doesn't interfere with plane controls, the plane will likely go forward longer. If, on the other hand, the pilot's body say falls on the controls, it may even disengage the autopilot if present and force the plane to make a move that will eventually go over its physical limits and results in spiral, stall, dive or disintegration in the air.