We take a null hypersurface (causal horizon) generated by a congruence of null geodesics as the boundary of the Doran-Lobo-Crawford spacetime to be the place where the Brown-York quasilocal energy is located. The components of the outer and inner stress tensors are computed and shown to depend on time and on the impact parameter b of the test-particle trajectory. The spacetime is a solution of Einstein’s equations with an anisotropic fluid as source. The surface energy density σ on the boundary is given by the same expression as that obtained previously for the energy stored on a Rindler horizon. For time intervals long compared to b (when the stretched horizon tends to the causal one), the components of the stress tensors become constant.