We examine the financial stability implications of covered bonds. Banks issue covered bonds by encumbering assets on their balance sheet and placing them within a dynamic ring fence. As more assets are encumbered, jittery unsecured creditors may run, leading to a banking crisis. We provide conditions for such a crisis to occur. We examine how different over-the-counter market network structures influence the liquidity of secured funding markets and crisis dynamics. We draw on the framework to consider several policy measures aimed at mitigating systemic risk, including caps on asset encumbrance, global legal entity identifiers, and swaps of good for bad collateral by central banks.