Verifiers play a central role in large language model reasoning by providing reliable supervision for post-training methods such as reinforcement learning. In code generation, however, verification is still predominantly based on fixed test cases, offering a narrow but underexploited form of verifiable supervision. We explore how existing test cases can be reformulated into more diverse and challenging sources of verifiable training signals. We propose Code-TVT (Test-Case-Driven Verifiable Tasks), a data synthesis framework that transforms program test cases into intrinsically verifiable code reasoning tasks. Using test cases already available in programming problems, we design two complementary tasks: Edge Test-Case Generation, which constructs edge-case inputs that expose subtle correctness failures, and Input Reconstruction via Program Output Inversion, which reasons backward from outputs to plausible inputs under execution-based verification. Experiments show that training with Code-TVT consistently improves code generation performance on three time-windowed LiveCodeBench splits (LCB-2408-2411, LCB-V5, and LCB-V6) under rejection-sampling fine-tuning and Group Relative Policy Optimization.