This type of loan is undertaken by companies that desperately need cash. It is called a death spiral because companies' stocks often plunge drastically after they take on these types of loans. It is important to note that death spirals often allow buyers to convert the bonds into shares at a fixed conversion ratio in which the buyer has a large premium.
For example, a bond with a face value of $1,000 may have a convertible value of $1,500, which means that a bondholder will receive $1,500 dollars worth of equity for giving up the $1,000 bond.
However, upon a conversion, more shares are created, which dilutes the share price. This drop in price may cause more bond holders to convert, because the lower share price means that they will be receiving more shares. Any further conversions will cause more price drops as the supply of shares increases, causing the process to repeat itself as the stock's price spirals downward.