Organizations often need to deal with ambiguous threats, which are complex, unprecedented, and difficult-to-predict events that hold the potential to cause harm. Drawing on the attention-based view of work behavior, we propose that employees do not always remain vigilant to such threats. Consequently, we argue that, in the face of those threats, employees can fail to notice or recognize problems or vulnerabilities in their organizations' work processes or products that can hinder coping. We posit that this effect is, paradoxically, more pronounced when employees are working with trustworthy managers who are perceived as capable and focused enough on the well-being of their units to adequately deal with work challenges. Thereby, we highlight that employees may overlook problems and thus not speak up, precisely when their input is highly desired to address ambiguous threats and can be effectively used by competent and caring managers. Using a combination of field surveys and preregistered experiments, we demonstrate support for our arguments. In the process, we present an alternative attention-based perspective to the voice literature that has so far predominantly focused on cost-benefit-based explanations (i.e., how employees evaluate the perceived costs of speaking up vs. presumed benefits) when describing hurdles to employee voice. (PsycInfo Database Record (c) 2024 APA, all rights reserved).