Indirect methods have proven to be a complementary approach for extending our knowledge of nuclear structure and low-energy cross sections. Among these, the neutron-induced reaction cross sections appear to be of particular interest since their role both for unstable and stable beams. In view of this, we report here the combined study of the 17O(n, α)14C reaction accomplished by the Trojan Horse Method (THM) and the asymptotic normalization coefficient (ANC) method. The low-lying 8038, 8125, 8213, and 8282 keV resonances in 18O are studied, and their Γ n are derived. A comparison with recent direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigations, and shows new frontiers for neutron-induced reactions with radioactive ion beams. Moreover, we examined the impact of adopting the newly recommended 17O(n, α)14C reaction rate on asymptotic giant branch stars' nucleosynthesis. Our findings reveal significant variations (≳10%) in the production of the neutron-rich heavy isotopes sensitive to neutron density, underlining the neutron-poisoning effect of 17O on the s-process.