What vertical flight profile could be expected from an aircraft if the pilots were incapacitated?
Emergency descent (like during a decompression event where you need to get from cruise to 10k ft ASAP to make sure the people in the back survive) shouldn't make a nice curve. It only wastes time you don't really have.

Normal operation means the pilot activates the autopilot during cruise which will fly the programmed course set by the pilot. It will stay follow that course (or put itself in a holding pattern on the final fix) until it runs out of fuel or the pilot intervenes when it is cleared for descent. This happened with Helios Airways Air flight 522; both pilots were incapacitated shortly after ascent and the plane put itself in a hold and crashed when it ran out of fuel after more than an hour.

A plane where there is nothing controlling the altitude (when control is lost due to loss of hydraulics for example) will follow a phugoid cycle. That is a series of dives and climbs as the elevators gain and lose bite on the air with speed.