Correlation between bond and liability

In asset allocation, page 109 (printed book), says:

“Bonds are inversely correlated with changes in the present value of the frozen liability cash flows (because the liabilities indicate negative cash flows)”.

But, in the next page, page 110, blue-box 16, answer 3 says:

"The observed relationship that the allocation to corporate bonds declines with increasing surplus return can be explained by the positive correlation of bond price with the present value of liabilities.:

I am really confused!!! can someone please clarify the correlation between bond and liability (Frozen/not frozen)?