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Existing algorithms for generating Counterfactual Explanations (CXs) for Machine Learning (ML) typically assume fully specified inputs. However, real-world data often contains missing values, and the impact of these incomplete inputs on the performance of existing CX methods remains unexplored. To address this gap, we systematically evaluate recent CX generation methods on their ability to provide valid and plausible counterfactuals when inputs are incomplete. As part of this investigation, we hypothesize that robust CX generation methods will be better suited to address the challenge of providing valid and plausible counterfactuals when inputs are incomplete. Our findings reveal that while robust CX methods achieve higher validity than non-robust ones, all methods struggle to find valid counterfactuals. These results motivate the need for new CX methods capable of handling incomplete inputs.