Neural stem cells (NSCs) are key physiological components of adult vertebrate brains, generating neurons over a lifetime. In the adult zebrafish pallium, NSCs persist at long term through balanced fate decisions that include direct neuronal conversions, i.e., delamination and neurogenesis without a division. The characteristics and mechanisms of these events remain unknown. Here we reanalyze intravital imaging data of adult pallial NSCs and observe shared delamination dynamics between NSCs and committed neuronal progenitors. In a candidate approach for mechanisms predicting NSC decisions, we build an NSC-specific genetic tracer of Caspase3/7 activation (Cas3*/Cas7*) in vivo and show that non-apoptotic Cas3*/7* events occur in adult NSCs and are biased towards neuronal conversion under physiological conditions. We further identify the transcription factor Atf3 as necessary to express this fate. Finally, we show that the Cas3*/7*/Atf3 pathways are part of the processes engaged when NSCs are recruited for neuronal regeneration. These results provide evidence for the non-apoptotic caspase events occurring in vertebrate adult NSCs and link these events with the NSC fate decision of direct conversion, important for long-term NSC population homeostasis.