Nigel: All the King's horses.
Bug: All the King's men.
This reference, used while they are listing the dead woman's body parts is alluding to the third line of the nursery rhyme Humpty Dumpty:
Humpty Dumpty sat on a wall.
Humpty Dumpty had a great fall.
All the King's horses and all the King's men
Couldn't put Humpty together again.
When Woody repeats "All the King's men" at the end of the episode, he is acknowledging the great work Nigel and Bug did for the widower.