Consistency-based repair is widely assumed to improve LLM-based document-level relation extraction (DocRE), but this assumption can fail when the benchmark itself is incompletely annotated. Whether such repair helps depends strongly on how closed the gold annotations are under the constraints it enforces. We introduce $Δ_{\rm closure}$, the rate at which gold annotations lack facts implied by the very rules used for repair, computable from the annotations and rules alone before any repair is run. The same typed constraints drive CONSISTRE, which applies them at inference time (constraint feedback for reflection, deterministic closure) and at training time (distillation and consistency-aware reinforcement learning). On 998 DocRED documents, whose Re-DocRED revision lowers $Δ_{\rm closure}$ from 1.71% to 0.257%, rescoring identical predictions reverses the method ranking: Self-Refine leads under DocRED, while a constraint-feedback variant moves from fifth place to first. On the near-closed DWIE, constraint feedback with chain-of-thought beats three generic reflection baselines by 0.046-0.107 micro-F1 ($p=0.0002$), and deterministic closure of the base output scores higher still at $3.6\times$ lower cost. A reinforcement-learning gain on DocRED (+0.025) does not survive Re-DocRED rescoring. Consistency repair pays off where annotations are closed, and $Δ_{\rm closure}$ tells in advance whether they are.

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