Anomaly-driven evaporation endpoints of a two-dimensional regular black hole

Spherical reduction of four-dimensional minimally coupled matter yields a two-dimensional theory with dilaton-coupled matter rather than minimally coupled conformal matter. We use this distinction to revisit the backreacted late-time endpoint problem for the regular two-dimensional Bardeen-like black hole considered by Barenboim, Frolov, and Kunstatter. Replacing the Polyakov quantum sector by the dilaton-coupled anomaly model of Fabbri, Farese, and Navarro-Salas (FFN), we derive the corresponding semiclassical field equations and classify the asymptotically allowed late branches at finite radius. For any quiescent finite-radius branch with finite nonzero conformal factor, the late-time mixed equation enforces $J'(r_\infty)=0$, and hence $r_\infty=\sqrt{2}\,\ell$, independently of the local dilaton-anomaly convention. For finite-radius null branches satisfying the stated state-tail assumptions, the ordinary strong-cosmic-censorship-restoring exponential null boundary is excluded. Generic power-law branches $e^{2\rho}\sim v^{-p}$ with $p>1$ are likewise excluded, except for the borderline case $p=2$, which is the only remaining null loophole of this type. In the FFN model, the settled realization of this loophole carries finite affine flux and requires the stronger state-tail decay $s_\phi=O(v^{-2})$. The natural finite-radius outcome is remnant-like, while the surviving null branch is a highly constrained soft-null alternative.