We investigate how long-range power-law interactions ($V\propto r^{-\alpha }$) influence the finite-size stability of many-body localization against boundary-induced thermalization in a one-dimensional disordered Heisenberg spin chain. Whereas previous studies have primarily examined avalanche instabilities through perturbative analyses or short-range models, we adopt an open-system approach that directly probes the dynamical response of a localizedlike regime to a controlled boundary thermalizing perturbation. By combining exact diagonalization of static properties with Lindblad master-equation simulations, we systematically examine the interplay among the interaction exponent $\alpha$, disorder strength $W$, and system size $L$. A finite-size scaling analysis of the half-chain entanglement entropy identifies an effective crossover near $\alpha \simeq 2$, separating a strongly long-range regime exhibiting enhanced delocalizing tendencies from a short-range-like regime with more robust localization signatures. To characterize avalanchelike dynamics, we couple one boundary of the chain to an infinite-temperature bath that serves as a minimal thermalizing seed and monitor the resulting bath-induced decay of the staggered magnetization imbalance. Within the accessible system sizes and simulation times, the characteristic threshold time is well described by the empirical scaling relation $T_{r_{\mathrm{th}}}\sim exp\left[\kappa \left(\alpha \right)LW\right]$, where the coefficient $\kappa \left(\alpha \right)$ increases monotonically with increasing interaction exponent. This trend demonstrates that shorter-range interactions provide substantially stronger resistance to boundary-induced thermalization in the strongly disordered regime. Motivated by this scaling behavior, we introduce an interaction-dependent disorder scale $W_{\mathrm{stab}}\left(\alpha \right)$ as an operational measure of avalanche resistance. Rather than representing a sharp thermodynamic phase boundary, this quantity provides a conservative, protocol-dependent characterization of finite-size dynamical stability. Our results show that long-range interactions facilitate bath-induced thermalization, whereas increasing the interaction exponent significantly enhances the robustness of localizedlike behavior against boundary perturbations.

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• Many-body localization
• Open quantum systems
• Disordered systems
• Exact diagonalization