Examples exist built from calls, puts, straddles, and variance swaps. Consider a hypothetical example in which an index holds two stocks in equal halves and implied correlation is 0.6. If realized correlation is 0.4, the index variance comes out lower than priced, and the party that sold the index variance swap and bought the constituents' variance swaps makes a profit. If realized correlation is 0.8, that party takes a loss.
Profit and loss from moves in the individual stocks that differ from what was priced also enters, so correlation is not the only source of profit and loss.