A floorless bond is a bond whose terms allow purchasers to convert them to common stock, as well as any accrued interest. The reason for its “death spiral” nickname is that bond holders can convert some shares and sell them on the open market, thereby supposedly driving down the price and allowing them to buy more shares, and so on. If a major bond holder were to convert all of its holdings to common stock, the result could be a major stock price decline, possibly resulting in a change of control in favor of the former bond holder. This situation is more likely to arise when several holders of a company's bonds, who control a large part of all bonds in aggregate, engage in this behavior to achieve a hostile takeover.
However, this conversion problem can be controlled to some extent by including conversion terms that only allow bond holders to convert at certain times or with the permission of company management.