'stiff' is 30s slang for a working class person (as in 'working stiff'). This would be like saying 'he really lucked out!' today - a mixture of admiration and mild jealousy for someone's (possibly unearned) good fortune.
I'm pretty sure stiff is slang for dead person, but it gets used more generally than that, for example: 'working stiff', a working person nothing going for him.
Does anyone know what that means?