In the case of a mortgage or auto loan, the issuer is the borrower and is the party that benefits from the prepayment option. In a declining interest rate environment, the issuer can retire higher cost debt and replace it with lower cost debt (i.e. refinancing a mortgage). When an issuer (borrower) calls, or prepays, the lending institution (the security holder) faces reinvestment risk because it must reinvest the proceeds at lower rates.
Mortgage backed and other asset backed securities have high reinvestment (or prepayment) risk because in addition to cash flows from periodic interest payments (like bond coupons), these securities have repayment of principal. The lower the interest rate, the higher chance that the loans underlying these assets will repay in full due to refinancings. A bond, such as a zero coupon bond, can have high interest rate risk (because its single cash flow subjects it to the full amount of discounting when interest rates change) and low reinvestment risk (the single cash flow minimizes prepayment risk).