Debugging consumes a substantial portion of the software development lifecycle, yet researchers do not yet understand well the effectiveness of Large Language Models (LLMs) in this task. Competitive programming offers a rich benchmark for such evaluation, given its diverse problem domains and strict efficiency requirements. We present an empirical study of LLM-based debugging on competitive programming problems and introduce DePro, a test-case-driven approach that assists programmers by correcting existing code rather than generating new solutions. DePro combines brute-force reference generation, stress testing, and iterative LLM-guided refinement to efficiently identify and resolve errors. Experiments on 13 faulty user submissions from Codeforces demonstrate that DePro consistently produces correct solutions, reducing debugging attempts by up to 64% and debugging time by an average of 7.6 minutes per problem compared to human programmers and zero-shot LLM debugging.