How did "stiff" mean cheating someone?
When someone gets taken advantage of, we would say "he got stiffed", where "stiffed" means "cheated".
What is the etymology of the word "stiff" used this way?
stiff
late 14c., "to make stiff," from stiff (adj.). Meaning "fail to tip" is from 1939, originally among restaurant and hotel workers, probably from stiff (n.), perhaps in slang sense of "corpse" (because dead men pay no tips), or from the "contemptible person" sense. Extended by 1950 to "cheat."
It appears that to cheat is derived in the 50's from its original meaning.