Could a "missing phase" result in damage to electrical household equipment=
If you do have 3 phase power loss of 1 phase cause what is called "single phasing". Sometimes a motor can run with the loss of 1 leg but it may start in the wrong direction and another time start in the correct direction. The motor will draw more than normal current on the working legs and usually overheats. With a heat pump single phasing can damage the compressor by starting in the wrong direction.