Does demand for safety create instability ? Secured (repo) funding can be made so safe that it never runs, but shifts risk to unsecured creditors. We show that this triggers more frequent runs by unsecured creditors, even in the absence of fundamental risk. This effect is separate from the liquidation externality caused by fire sales of seized collateral upon default. As more secured debt causes larger fire sales, it leads to higher haircuts which further increase the frequency of runs. While secured funding combined with high yield unsecured debt may reduce instability,the private choice of repo funding always increases it. Regulators need to contain its reinforcing effect on liquidity risk, trading off its role in expanding funding by creating a safe asset.Key words: