With the success of transformer architectures across diverse applications, the error correction code transformer (ECCT) has gained significant attention for its superior decoding performance. In spite of its advantages, the error floor problem in ECCT decoding remains unexplored. We present the first investigation into this issue, revealing that ECCT encounters error floors, limiting its effectiveness in practical settings. To address this error floor problem, we adopt a hybrid decoding framework that integrates ECCT with conventional hard decision decoders. Unlike prior hybrid decoding schemes, our key contribution lies in proposing a novel loss function that explicitly takes into account the interaction between ECCT and hard decision decoders during training. The proposed loss function guides ECCT to focus on residual errors that are not corrected by the hard decision stages, effectively lowering the error floor. Simulation results confirm that the hybrid decoder trained with the proposed loss function achieves substantial performance gains over standard ECCT in both the waterfall and the error floor regions.