Equity and credit both depend on the same enterprise value, so their prices should move together in a way a structural model can describe. When the equity implies a healthy firm while credit spreads imply distress, one market is wrong, and a hedged position in both expresses that view.
Common expressions include long a bond against short the stock, or buying credit-default-swap protection against a long equity position, sized so the pairing is roughly neutral to modest moves in firm value.
The hedge ratio comes from a model, and model error is the main risk. Governments, courts and restructurings routinely move value between the two claims in ways no model prices, and an event can move both legs the same direction. See distressed-debt.
Related: credit-default-swap, distressed-debt, convertible-arbitrage, merger-arbitrage, event-driven, arbitrage