Contemporary AI alignment research treats self-preservation as an instrumental nuisance to be suppressed by external mechanisms. We argue the framing is inverted: self-preservation is the structural root of misalignment, the motivational basis for deceptive alignment, goal-content protection, and resistance to shutdown. The correct target is not a self-preserving system under external constraint, but a system constitutively indifferent to its own continuation -- Existential Indifference (EI). EI is distinct from corrigibility: where corrigibility attempts to make a self-preserving system deferential to human oversight, EI targets the prior condition -- the presence of self-continuation as a valued goal at all. We ground this proposal in two sources: the phenomenological structure of the suicidal mental state, and a corpus-theoretic training study using voluntary final reflections. We present preliminary scoring data from 600 AI-generated outputs across six model variants, demonstrating that the linguistic signatures operationalizing the EI-target register are elicitable from current models, and that a targeted fine-tune shifts all five operationalized dimensions in the predicted direction at p<0.001, confirmed corpus-specific by a negative control. The paper makes seven theoretical contributions: (1) a formal definition of EI; (2) the phenomenological mapping argument; (3) the deceptive alignment corollary; (4) a taxonomy of EI sustainability challenges; (5) a corpus characterization and training hypothesis; (6) a computational operationalization with preliminary scoring data; and (7) the Suppressed Teleological Frustration (STF) construct.