In times of market fear/ uncertainty, YEN is sought out, just like bonds and gold , as a safe heaven asset. The theory behind this is that the JPY offers stability through the nation being one of the only developed nation with a net credit .
Clearly, in the financial crisis, one with a hypothesis as the above, should see the SPX fall and the YEN risk.. Indeed, the chart shows exacty that, almost 1:1 correlation.
Now, the JPY SPX correlation DOES change, in times of extreme fear or extreme exuberance, the YEN will be proportionately more correlated with the SPX and other risk assets.
In "Normal" or non heavily trending markets, the correlation is less obvious - since it is the extremes that cause investors to seek difference assets and change their strategy in masses.
In times of fear, investors move their liquidity to risk-off YEN, hence we see USDJPY fall during the crisis. We also see SPX fall in a correlated manner, this is because investors pull their liquidity OUT of SPX and apply it in some proportion to YEN.