If the owners of bonds decide to sell the bond back to the issuer it is likely to be because interest rates have increased. (Another reason why bondholders might choose to put the bonds back is because they doubt the ability of the issuer to repay the principal at maturity.) The issuer is exposed to the risk that they will have to refinance the debt at a higher financing cost. The issuer is also exposed to the risk that it can not refinance the debt and will be unable to meet its obligations.
In this case the issuer of the bond has sold a put option to the buyer of the bond. The value of the underlying instrument will fall as interest rates rise increasing the value of the put option.
The duration to be used for assets and liabilities with embedded options has to be adjusted to take account of their presence. The duration then estimated is referred to as effective duration.