The loss of a companion animal can provoke grief whose intensity rivals human bereavement, yet its biological basis remains largely uncharted. This structured narrative review synthesizes neurobiological, endocrinological, immunological, and psychosocial evidence into a mechanistic framework offered not as established fact but as a source of testable hypotheses. We trace the substrates of the human-animal bond across six interacting systems and propose how disruption of each upon an animal's death may drive grief. Three carry comparatively robust analogical support (oxytocinergic signaling, hypothalamic-pituitary-adrenal [HPA] axis regulation, and neuroinflammatory activation) and three are more exploratory (dopaminergic, serotonergic, and endocannabinoid pathways). Integrating extracted study-level data into transparent prioritization heuristics, we identify the HPA axis, assessed with its coupled oxytocinergic partner, as the most defensible first target for a direct biomarker study, a conclusion robust across three methodologically independent analyses. No direct pet-loss evidence yet supports any proposal, and this gap is the review's central motivation. As applied context, we address euthanasia-related guilt, disenfranchised grief under East Asian norms (a tentative "double disenfranchisement" hypothesis we want tested), assessment instruments, evidence-graded therapies, a Korean tool-development roadmap, and One Health research priorities.