At that point, he can reinvest it for a period of one year. If rates are high when the bond matures, he should be able to make the liability payment. He will probably even have a surplus. If rates drop, though, he might not have enough money to make the payment. The investor has left himself open to interest rate risk, but in this case it is not the price risk that we saw earlier.
Reinvestment risk is another form of interest rate risk.
Duration can still be used to measure this risk, as long as there is either an investment horizon or a stream of liabilities involved. Since the asset's duration is shorter than that of the liability, we can infer that there is reinvestment risk rather than price risk. If rates go up during that period, the price of the bond will fall. But the investor is insensitive to this, because the present value of the liability also falls by an equal amount. Similarly, if rates go down then he is insensitive to the reinvestment rate, because he will not be reinvesting any cash flows during that period.