OK, one more situation where you need to remove a chip,
and do not want to destroy either the chip nor the PCB:
Had an IBM MDP board that had intermittent screen data corruption when
scrolling. On close examination, found that it had originally been
assembled with one pin of one chip bent under, instead of through the
board and soldered. Desoldering the chip, and resoldering it with ALL of
the pins properly connected fixed it.