TLDR:
Changes to the conversion privilege during the life of an issue are commonly made to either decrease the conversion price, which protects the holder from "dilution," or to increase the conversion price for the benefit of the company based on a sliding-scale arrangement. However, when the sliding scale is based on the extent to which the privilege is exercised, a conflict arises in the holder's mind between seniority and early conversion due to limited opportunities. This can lead to forced conversions.
If an issue is convertible into preferred stock, the maximum benefit from such a privilege is likely to be kept to a modest figure due to an upper limitation on the market value of the preferred stock. Bonds that are convertible at the option of the company are, essentially, a junior issue that will be converted, disguised as a bond.