Let $(M^n,g(\tau))$ be a connected complete backward Ricci flow on an interval $I\subset(0,t_0]$ with bounded curvature on compact subintervals, finite reduced volume, and reduced distance $l: M \times I \to \mathbb{R}$ based at a regular point. Let $\widetilde V: I \to [0,\infty)$ denote the associated reduced volume. If $\widetilde V$ is constant on $I$, then on the regular spacetime region generated by minimizing $\mathcal L$-geodesics from the basepoint, before their cut time, the flow is, after pulling back by diffeomorphisms and parabolic rescaling, the canonical backward flow of a gradient shrinking Ricci soliton. Conversely, the canonical backward flow generated by a complete gradient shrinking Ricci soliton with normalized potential has constant reduced volume.