The concept of extinction debt refers to the time-delayed extinction of species following an environmental change. Precisely because of their delayed nature, extinction debts constitute a major challenge for both biodiversity research and conservation. Although it has received considerable attention and support from theoretical and empirical evidence during the last decades, the concept is still mainly apprehended through a species-based view. However, our understanding of ecological systems is increasingly enhanced by approaches focusing on ecosystem functioning and species interaction networks. Notably, co-extinctions triggered by the loss and disruption of species interactions has received growing interest. Yet, the wide spectrum of potential co-extinctions is rarely considered through the lens of transient dynamics. A more ecosystem functioning-focused perspective on delayed extinctions is thus needed. Here, we propose to fill this conceptual gap by revisiting the concept of extinction debt in the light of multitrophic networks and meta-ecosystem theories. We emphasize the coupled nature of ecological dynamics across interaction networks within and between ecosystems, which the current view of extinction debts does not fully integrate. We address how the structure of interaction networks and the contrasting tempo of extinction in species, function and interaction can determine co-extinction debts scenarios. Importantly the alteration of specific organisms and ecological processes can trigger ecosystem-level feedbacks and lead to cascading delayed co-extinction dynamics spreading across ecological networks. We argue that such transient dynamics are likely to incur both long-term and remote consequences on biodiversity and ecosystem functioning. Then, we outline the challenges and opportunities for research and conservation emerging from this new perspective on extinction debts.