We can almost think of this as a game between two opponents. The holder of the bond tries to maximize its value at all times. The issuer of the bond tries to minimize its value. Protected call and unprotected call. A certain bond may become callable by the issuer as of a certain date.
Many bonds have some unprotected calls and some calls that are protected.
Conversion into shares and cash. In many cases, the conversion number as well as the cash amount vary as a function of time. Some convertibles have put features that could increase their value. When an investor converts and receives shares, the shares may either be distributed from an existing stock or there might be new shares printed. There are now more company shares for the same capital base.