I've had iron golems keep swinging at the ground after killing a skeleton. I've had skeletons keep shooting at the empty space after they killed the iron golem. They stop doing this if you save and quit the game and come back.

To reproduce, give a skeleton full diamond armor with protection 4 or 3. Make a golem, and splash it with weakness, maybe damage it a bit. The skeleton should kill the golem once attacked. It will then continue to shoot at the same spot forever (if it has no new targets, not attacked, etc).