This study investigates whether war-induced forced migration has led to persistent imbalances in Eastern European labor markets, with a specific focus on matching efficiency. The analysis utilizes a quasi-experimental design combining Eurostat and UNHCR quarterly panel data for the EU-27 from 2014 to 2025. The methodology employs a multi-period difference-in-differences approach and Beveridge curve regressions to isolate the specific impact of the Temporary Protection Directive flows. The findings indicate an upward and outward shift in the Beveridge curve following the 2022 shock, characterized by a simultaneous increase in vacancies and unemployment. The results demonstrate that high institutional integration capacity dampens these shock effects, while persistence primarily observed in service-intensive sectors. The study suggests that reducing matching costs through targeted language equivalence accelerators and fair placement algorithms is essential for market stabilization.