We investigate the optimal prediction of a firm's long-term financial distress endpoint, which is modelled as the last passage time $l_r$. More specifically, it represents the right endpoint of the last negative excursion lasting longer than a constant $r>0$. For a Brownian motion with drift $\mu>0$ and volatility $\sigma>0$, our goal is to identify an optimal stopping time that minimizes the ($L_1$) distance from the last passage time $l_r$.

We find that the optimal stopping barrier exhibits two distinct structures (a constant barrier or a moving barrier characterized by the unique solution to an integral equation) depending on the ratio $R=\frac{\mu\sqrt{r}}{\sigma}$ which integrates a firm's financial profitability, instability, and risk tolerance to financial distress. To obtain the optimal stopping time, we examine the smooth fit condition, Lipschitz continuity of the barrier, and probability regularity of the boundary points. Our results imply that a firm should postpone advancing strategic plans (e.g., paying dividends and expanding business) if the firm has low profitability, high instability, and low tolerance level of insolvency.