The China Airlines Airbus Industrie A300B4-622R accident at Nagoya, Japan on 26 April 1994 is an example of the possible consequences of a conflict in goals between the autoflight system and the flightcrew. The description below is from the accident report:

Aircraft Accident Investigation Commission - Ministry of Transport Japan (1996). China Airlines Airbus Industrie A300B4-622R, B1816 Nagoya Airport April 26, 1994. Tokyo: Ministry of Transport.

 China Airlines Airbus Industrie A300B4-622R B1816 took off from Taipei International Airport at 0853 UTC (1753 JST) on April 26, 1994 and continued flying according to its flight plan. About 1116 UTC (2016 JST), while approaching Nagoya airport for landing, the aircraft crashed into the landing zone close to E1 taxiway of the airport. ... While the aircraft was making an ILS approach to Runway 34 of Nagoya Airport, under manual control by the F/O, the F/O inadvertently activated the GO lever, which changed the FD (Flight Director) to GO AROUND mode and caused a thrust increase. This made the aircraft deviate above its normal glide path. The APs were subsequently engaged, with GO AROUND mode still engaged. Under these conditions the F/O continued pushing the control wheel in accordance with the CAP's instructions. As a result of this, the THS (Horizontal Stabilizer) moved to its full nose-up position and caused an abnormal out-of-trim situation. The crew continued approach, unaware of the abnormal situation. The AOA increased, the Alpha floor function was activated and the pitch angle increased. It is considered that, at this time, the CAP (who had now taken the controls), judged that landing would be difficult and opted for go-around. The aircraft began to climb steeply with a high pitch angle attitude. The CAP and the F/O did not carry out an effective recovery operation, and the aircraft stalled and crashed. ... On board the aircraft were 271 persons: 256 passengers (including 2 infants) and 15 crew members, of whom 264 persons (249 passengers including 2 infants and 15 crew members) were killed and 7 passengers were seriously injured. The aircraft ignited, and was destroyed.