Multimodal human activity recognition (HAR) and human pose estimation (HPE) must cope with modalities missing at inference. Completions generated for a fixed fusion model must preserve the fusion readout: what fusion uses from each modality. We propose COMPASS, a completion-and-fusion framework in which each modality occupies a fixed slot filled by an observed representation or a completion inferred from available inputs. Its core principle, fusion-matched supervision, supervises completions with same-sample real targets at readout granularity: token means for HAR, where fusion averages tokens, and per-joint representations for HPE, where fusion preserves joint structure. Trained with complete multimodal samples, COMPASS improves subset-averaged performance over the strongest baselines on XRF55 and MM-Fi for HAR and on MM-Fi for HPE. At fixed architecture, fusion-matched supervision outperforms full-token and centered-token matching in HAR, and joint-mean matching and no matching in HPE. The code is available at: https://github.com/haowangcoder/COMPASS.

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