Distinguish or Homogenize: Last-Chance Policy Identification and Risk-Budgeted Recovery under Irreversible Resource Depletion

Under irreversible resource depletion, an agent can spend resources to distinguish among latent fault models, or to change the system state so that the remaining models admit a common acceptable continuation--at which point further diagnosis becomes unnecessary. This distinguish-or-homogenize principle identifies a path that existing frameworks for identification, planning, and diagnosis do not make explicit: prior formulations treat the mapping from fault models to acceptable policies as a given, whereas LCPI makes it a function of the agent's own actions. We formalize this principle through Last-Chance Policy Identification (LCPI), where correctness is evaluated at the state the agent reaches rather than at the initial state. The Last Identifiable Margin (LIM) marks the feasibility boundary between distinguishing and homogenizing. For deterministic diagnostic graphs we provide the Exact-LIM recursion; for noisy finite-horizon recovery we propose Risk-Budgeted Compatibility Planning (RBCP), which searches a compatibility-aware frontier under a hard worst-case failure constraint. Across incident recovery on abstract microservice topologies and latent-damage navigation in MiniGrid, RBCP improves risk-feasible recovery while satisfying the failure budget. A sham control--cost-matched actions that preserve model incompatibility--eliminates the gain entirely, confirming that the benefit comes from changing which policies are acceptable for which models, not from extra search or additional budget.