Abstract Basque displays what is known as the Strong Person Case Constraint (PCC): an absolutive DP may generally not be 1st or 2nd person if it is c-commanded by a dative DP. We make the novel observation that this restriction is obviated under verbal ellipsis, even if this ellipsis does not affect the DPs whose cooccurrence is normally ruled out. We then explore the consequences of this generalization for accounts of the PCC. First, it indicates that the PCC arises from properties of the verb agreement, not of the DP arguments. Second, a comprehensive account of the Basque PCC must be sensitive to both narrow-syntactic and PF properties (in particular whether or not the verb agreement is pronounced). We then develop an account of the Basque PCC based on Coon and Keine’s (2021) feature-gluttony proposal. On this account, the Basque PCC results from an irresolvable conflict that arises in the morphological realization of a probe that has agreed with two DPs. We show that such an account offers a principled explanation of both the syntactic factors and the PF factors that condition the Basque PCC, in particular its interaction with verbal ellipsis.