The beginning of GF (and the novel) is full of parables about Mob life. Paulie's story is a good one: Betrayal is never far away from any Don's existence. And, greed makes otherwise smart people stupid.
Paulie was an up-and-coming button man who was due for a reward (says the novel) for carrying out the beating of the two punks perfectly. His greed cost him his life--and nearly cost Vito his life.