Despite the identification of numerous regulators of regeneration in different animal models, a fundamental question remains: why do some wounds trigger the full regeneration of lost body parts, whereas others resolve by mere healing? By selectively inhibiting regeneration initiation, but not the formation of a wound epidermis, here we create headless planarians and finless zebrafish. Strikingly, in both missing-tissue contexts, injuries that normally do not trigger regeneration activate complete restoration of heads and fin rays. Our results demonstrate that generic wound signals have regeneration-inducing power. However, they are interpreted as regeneration triggers only in a permissive tissue context: when body parts are missing, or when tissue-resident polarity signals, such as Wnt activity in planarians, are modified. Hence, the ability to decode generic wound-induced signals as regeneration-initiating cues may be the crucial difference that distinguishes animals that regenerate from those that cannot.