Background/Objectives: Referral-based and hospital-based disease registries may contain high-quality data on registered patients while incompletely and differentially capturing the eligible case population. We developed an identification framework that separates post-capture problems from genuine ascertainment problems and links population correction to the information available about uncaptured cases. Methods: The framework was informed by a targeted methodological synthesis and evaluated using Monte Carlo simulations of 5,000 eligible cases over 1,000 replications. We examined non-differential capture, differential capture depending on measured covariates, residual capture depending on an unmeasured determinant, and a separate two-source capture-recapture experiment under independent and positively dependent capture. Results: Under measured-covariate differential capture, the registry prevalence had mean bias of −0.0277, whereas valid external standardization and inverse-probability selection weighting reduced mean bias to 0.0001. When capture also depended on an unmeasured determinant, X-only correction remained biased (0.0184). Under independent two-source capture, the Chapman estimator was approximately unbiased for N=5,000 (mean 4,998.9), whereas positive source dependence produced substantial downward bias (mean 3,936.4). Conclusions: Direct population identification may arise from eligible-case target data, valid capture probabilities, or overlapping sources, whereas general-population covariate margins and indirect completeness indicators are generally insufficient on their own. Incomplete case ascertainment should therefore be addressed by matching the inferential target to the information that identifies it.