A body of psycholinguistic research shows that structural constraints play a large role in guiding anaphora resolution in the early moments of processing (Nicol and Swinney 1989; Harris et al. 2000; Sturt 2003; Kazanina et al. 2007; Xiang et al. 2009; Chow et al. 2014). Omaki (2010) and Omaki et al. (2019) report on an interesting case where reflexives in wh-predicate fronting constructions launch a search that is not structurally guided. We further investigate this phenomenon, by asking whether non-structurally guided retrievals of this sort result in comprehenders ever committing to ungrammatical antecedents, perhaps as a ‘lingering’ interpretation of the sort found with garden path sentences (Christianson et al. 2001; Ferreira et al. 2001; Slattery et al. 2013). In two forced-choice studies, we find evidence that ungrammatical dependencies resulting from a non-structural search are sometimes maintained in offline comprehension, particularly with a more demanding task. We then probe the incremental processing that follows non-structurally guided retrieval, asking if and when the processor initiates a renewed search. In a self-paced reading experiment, we show that the processor continues its search for an antecedent very soon after retrieving a non-structurally guided antecedent. Surprisingly, however, we found a similar processing profile in cases where a structurally licensed antecedent was already encountered. While it has been recently shown that cataphoric pronouns persist in an antecedent search after a failed retrieval (Giskes and Kush 2021), our results suggest that when reflexives locate a preceding antecedent – by either a structural or non-structural search – this does not terminate further consideration of a different dependency. We consider these data in light of the comparison between cataphoric elements and wh-fillers in launching an active search to complete a dependency.